So basically, a Jeffersonian Democracy isn't a form of Democracy per se, but an organization of power within a Democracy. The United States is a Federation, which means it's something akin to a series of small nations or "States" that have ceded certain powers to a larger government body (The United States, for our purposes, the Federal government). States in turn represent smaller governments within its body (local governments) which in turn represent individuals who live within the local government.
Order from most inclusive to least inclusive, we get: Federal, State, Local, Individual.
I order by inclusion because, Jeffersonian Democracy is a school of though about which is more powerful or should have more power. Pre-Civil War, the two political parties were divided over just how much power each government should have. At its core, a Jeffersonian Democracy affords as much freedoms and rights to the citizens and imposes more and more restrictions on each level of government above the individual level. It's also the philosophy that the Government is a necessary evil and needs to be heavily checked, monitored, and impeded against in order for it to perform proper functions (common defense, protection of rights, etc) without becoming a tyrannical monster.
It is opposed by Federalists, who believed that the federal level should hold more power and feared a mob rule that might occur if individuals thought they new better than the educated elected politician. They also supported foreign relations with England and respected standing governments in Europe (they were opposed to the French Revolution). Jeffersonians supported an "Empire of Freedom" and nations that sought Democratic Revolution (such as in France) and were still fearful of British Power. There foreign Policy was to be friendly to all nations and avoid alliances, fearing that they might have to commit to actions that compromised American ideals and may commit us to support a regime over a nation's citizens.
If you read the Constitution, the powers of the Federal Government are limited in the Articles and further limited by the 9th Amendment which basically says that the people have more rights than the constitution says, but they don't want to narrow the scope by listing it all. The 10th Amendment basically says any power or right not specifically granted to the Federal Government by the Constitution is either a power or right of the state or the individual. This also means that all laws and regulations must comply with the Constitution.
Compared to the British Parliamentary system which which operates on the belief that Parliament sets the Ultimate Law of the Land, and can be changed by acts of Parliament. The Freedom of Speech in the UK is guaranteed by Parliament and is subject to change at Parliament's whims. In the United States, the Constitution says Freedom of Speech cannot be stripped from the people at any level of government unless the people will it overwhelmingly (enough support to change the constitution). Most Representative Democracies are also Constitutional (England and New Zealand are the only two nations in the world without a Constitutional document. Australia has several documents which form their Constitution.) and many of those are inspired by the United States Constitution.