When discussing political issues and parties, I often hear mention of a party being "left", "centre-left", "right" or "extreme right". In broad terms, what do these designations mean?
The standard terms of left and right politics originate from the seating arrangement of the French National Assembly of 1789. They are often considered overly simplistic for today's complex political landscape.
In the 1789 at the French National Assembly the First Estate (noblemen) sat on the right side and the Third Estate (revolutionaries) sat on the left side. Thus, the left wing of the room was more liberal, and the right wing was more conservative.
Today you often use the terms left or extreme-left to describe social and progressive measures and right or even extreme-right the more conservative and nationalistic approaches. Those terms as I stated in the first paragraph however are too simplistic for a modern world where libertarians are often very progressive (left) on social issues such as gay marriage but are fiscally very conservative (right).
To quote from my own answer on History SE, the terms "left" and "right" have no objective meaning in today's global politics (unlike their historical usages covered by other answers) - they are 100% subjective, AND extremely varied across polities even when attempted to be used objectively.
To give some examples of complete inconsistencies:
In post-USSR Russia communist hardline parties are considered "Right Wing" and pro-Western economically liberal ones (e.g. pro-capitalist) are "Left Wing".
A somewhat related but separate problem is historical drift. As a classical example, originally support for laissez-faire capitalism and free markets were counted as being "on the left"; today in most Western countries these views would be characterized as being "on the right".
Gay Rights are commonly considered a property of the Left Wing (and opposition to them Right Wing). Leaving aside the usual imprecision of lumping together people with diverse views with a simplistic label ("right wing" libertarians in USA are strongly anti-gay-discrimination), let's not forget that SA was strongly pro-homosexual all the way to the top (Rohm). Sturmabteilung wasn't exactly an example of what people commonly refer to "left wing", though technically speaking, being against the established order, they should be. Also, many Marxist/leftist governments (e.g. USSR, Cuba) were strongly anti-gay for a variety of reasons, some of which were... "being gay is a bourgeoisie thing".
It's very hard to define "Right Wing" today, especially since most people referred to as "Right Wing" today not only have nothing in common with the historical origin of the term (French Monarchists after French Revolution), but don't have much common politically with each other aside from opposing some or all of the policies labeled "Left Wing", and even that for a wide variety of reasons.
People lump together on the right anyone from staunchly anti-religious "sex maniac" Ayn Rand to "Family Values" Christian fundamentalists some of whom literally wouldn't agree with Randian Objectivists about anything other than statists/Communists being a common opponent.
Even single-country party affiliations don't help much either, for a variety of reasons. "USA Republicans are Right Wing" is a nice soundbite, except you just lumped together Ron Paul, Pat Robertson, Martin Luther King Jr., Trent Lott and Abraham Lincoln. Again, not really all THAT much in common between the 5 of them.
These terms vary greatly by country. In the US, currently "left" is identified with people that believe in:
- Redistribution of wealth by means of taxation and welfare spending
- Expansive treatment of rights - i.e. right to housing, right to specific level of income, right to medical care, etc.
- Positivist approach to rights (government can create or destroy rights)
- Laissez-faire governmental approach to social life and public morals
- Government control for the behaviors that are considered harmful to the society, and governmental encouragement of the behaviors that are considered beneficial for the society
- More diplomatic and appeasing approach to international conflicts
- Primacy of international law and mores over the national peculiarities and traditions
- Collectivism more than individualism
On the other hand, the "right" is identified with:
- Laissez-faire approach to economic activity
- Restricting the role of the government to ensuring economic activities are not violating the rules of "fair play" but not promoting any specific goals or activities
- Private responsibility for one's welfare
- Governmental and public control over morals and social life
- Great reverence to tradition, religion, etc.
- Negativist approach to rights (rights are absence of violation of small number of principles)
- More forceful and aggressive approach to international matters, including intervention in places that do not directly influence internal US matters
- Nationalism and primacy of national law and mores over the international ones
- Reducing taxation and discouraging using taxation for governmental projects beyond defense, internal policing and such
- Individualism more than collectivism
You may notice that some of these items seem somewhat contradictory or inconsistent, and some are vague. This is what it is - people do hold contradictory or inconsistent beliefs and some of their positions are vague or fluid. You may also notice many people that vote right hold some left views, and many people that vote left have right views. That happens a lot.
About the "extreme" and "far" labels - except for a small variety of cases (like neo-nazis, anarchist gangs and such) they usually mean exactly nothing. In 99.9% cases this label would be applied by a politician to an opposing politician and would mean no more than "this is a very bad man, you should vote for me, not for him".
Another interpretation of left and right that one may come across relates to the distribution of power. In a simplified way, the right is associated with a top-down power structure, whereas the left is associated with an egalitarian distribution of power. This distribution fits with what most people would associate with left and right in daily life.
Right-wing ideologies favour power structures that are top-down. This can be power by the church, the state, corporations, etc. The most extreme example of this are extreme-right ideologies such as fascism, which is the ideology of anti-democracy. Depending on interpretation of power, also models that allow for very large corporate freedom (such as anarcho-capitalism/libertarianism) are far right, because corporations are not normally democratically controlled. See also wage slavery.
The left, then, favours egalitarian power models. As society originates in top-down power models, such ideologies are often radical or revolutionary in nature. In its extreme, this can be expressed by the utopian German (double negative) slogan Keine Macht für Niemand, which literally means no power for nobody. The ideal expressed by this phrase is that nobody holds power over anybody else. This is not limited to politics, but also to other aspects of life, most notably at work. In such a distribution of power, work is not associated with shareholder-owned corporations, but with worker-owned cooperatives.
The division above is consistent with the traditional distribution of ideologies in left and right. Left-wing is big government and right-wing is small government, because in our society the government is more or less the only institution under some democratic control, so if power is transferred from a democratically controlled government to uncontrolled corporations, power becomes more top-down; if power resides with a democratically controlled government, power becomes more egalitarian. Of course, this breaks down if a government is not democratically controlled.
In this model:
- Fascism is far-right because it explicitly strives for a authoritarian distribution of power.
Anarcho-capitalism can be considered far-right because it takes away almost all power from democratically controlled organs, but whether this leads to a vertical distribution of power depends on where this power goes. If this power is taken by shareholder-owned corporations, it means power distribution becomes more vertical.
Theocratic systems favour a strong power for religious institutes. I think those are mostly hierarchical in nature; I'm not aware of strongly democratic religions. That would put theocracies on the right (see also conservative below).
Communism is far left in theory, because it puts workers in control of the factories and of the state. In practice it turned out quite authoritarian, so rather right-wing and in its extremes alarmingly close to its ideological opposite, fascism. However, even if the situation turned out similar in practice, the propaganda, what the nations claimed to be, was still vastly different between the worst era of Stalinism and fascist states.
Socialism and Social-democracy tend to empower workers, but to a lesser degree than communism, and are therefore less far left on the scale.
Anarcho-syndicalism is perhaps the most far left, approaching the utopia where nobody holds power over everybody else, by putting the means of production in hands of democratic councils, e.g. factories are owned by the workers etc. The power of the state is minimal, but contrary to anarcho-capitalism, this power is transferred to small-scale democratically owned organs, not to huge multinational shareholder-owned corporations.
Conservative ideologies tend to the status quo. The status quo is usually a quite top-down division of power, so those can be considered right-wing.
Progressive and revolutionary ideologies favour to change society. Most of those ideologies are on the left, such as communism and anarcho-syndicalism. However, nazism was also revolutionary in nature, although left-wing revolutionaries may choose to use the term reactionary, as nazism was also strongly anti-revolutionary in nature.
Now this interpretation is not unique, but I think it works well to describe most important ideologies. Your mileage may vary :)
During the French revolution the most radical politics were sitting on left site, the most conservative on the right. So traditionally the conservatists (the ones who want to preserve existing order) are considered rightists, while the people who want to change it are considered leftists.
This divide functions quite well in USA, where rightists (conservatists) are fighting for traditional American values such as right to possess arms and corporation-friendly law.
In Europe the situation is much more complicated. Where the Nazi rightists or leftists? They wanted to overthrow the existing order. But they are considered rightists, because they glorified the right of the strong over the weak. In Europe someone who cares for weak and want to protect them from stronger is considered leftist.
There comes also the attitude towards religion. The politics who consider religion as basis of social relations are considered rightists and those who oppose - leftist. However, there are christian-socialist parties which are both religious-driven and concentrated on the poorest and the weakest. On the other side we have radical liberal parties, which are both against religion and for the lower taxes and low social expenses, which are hard to classify as leftists or rightists.
While these criteria are normative, there are solidly defended norms out there for these meanings. A number of the other current norms have been covered, so I'm going to concentration on the broadly Marxist normative system for these terms that arises out of the issue of control over productive property in society.
Such a schema results is a very rapid classification: Those acting or claiming to be in favour of workers control of production: Left Those acting or claiming to be opposed to workers control of production: Right Those acting or claiming to be indifferent or deliberately seeking an accommodation between worker and boss that significantly empowers workers: Centre
In this scheme almost every political party lies between right-centrism and the far, but not revolutionary, right. Most current parliamentary "Communist" parties, such as Eurocommunism or most self-announced "revolutionary" Trotskyite parties are actually right-centrist. Their platforms describe minor adjustments to capitalism in favour of "fairness" or "it working better."
This comes across a number of problems in the post-1789 world, and can't functionally apply to a pre-1789 world (The Party and the Faction, for example); it pre-supposes a bourgeois triumph over the aristocracy in terms of the dominant mode of production and property form.
So what about reactionaries? Most 19th century reactionaries were supporting a kind of state led capitalist development, much like the fight over Corn between Tory and Whig.
The other major problem is the difference between ideology and practice by political parties. The simplest Marxist way to deal with the Bolshevik parties is to observe the vigorous critique of their substitutionalism prior to 1917—a large number of people knew what this party was—and the fight over what a ruling Bolshevik Party would look like, worker or boss, between 1917 and 1921. More interesting is the long term collapse to the right of Labourism; from a right-centrist to a centre-right movement, while there are some delightful early marxian analyses ("I believe the worker and their boss should keep their present station" IWW, "Bump me into parliament"), this tends to submerge the long march towards Blair of the UK party.
tl;dr: These meanings are dependent on a theoretical perspective, media commentators usually fail to announce their theoretical perspective, understanding the variety of theoretical perspectives present can let you discover which theory the analyst is using, above is an example of the Marxist theoretical perspective on left/right.
A great visualisation of the left vs. right concept can be found here:
Left vs. right visualisation (by David McCandless): http://www.informationisbeautiful.net/visualizations/left-vs-right-world/
Lose all hope upon entering the doors of categorization because you will leave the perspective of the whole ---how ever perplexing--- behind!
After this warning, i may confess that for this kind of questions i usually fall back to notes i took during a course of latin american history back in 1993.
So my answer to you in a nutshell is historically: "right wing means monarchist, while left wing means revolutionary" and actually: "right wing means conservative, while left wing means progressive".
To analyse social movements and ideologies you can add other axes to the historical one, e.g economic (all between socialism and capitalism) and politic (all between anarchism and authoritarianism). This way you may get a better picture of the whole.