In First Past The Post voting:
Voters put a cross on a ballot paper next to their favoured candidate and the candidate with the most votes in the constituency wins. – electoral-reform.org.uk
What does "The Post" refer to? It sounds intuitively like it would be a fixed figure (e.g. 50% of the electorate, or 50% of the votes), but as the winner needs only to have the "most votes," that is not so. If it is an analogy to horse racing, where there is a fixed post to pass, please explain the analogy.
"First Past The Post" voting is simply "whoever gets the most votes". A common system used in most of the US and UK, for example.
The 'post' in this case is having the 'most votes'. It's not a fixed number at all. Whoever has more votes than anyone else, wins. It's not always a majority.
In many cases, a majority of votes isn't needed to win--simply having more votes than anyone else is enough to give you the win. In some cases where there is a desire to have an actual majority of votes, then there may be multiple rounds of this type of voting used in a run-off system.
As for the analogy, that part might be better asked on english.se. But yes, in simple terms, it's simply using the metaphor of a horse race.
The term first past the post (abbreviated FPTP or FPP) was coined as an analogy to horse racing, where the winner of the race is the first to pass a particular point (the "post" or finish line) on the track (in this case a plurality of votes), after which all other runners automatically and completely lose (that is, the payoff is "winner-takes-all").
There is, however, no "post" that the winning candidate must pass in order to win, as the winning candidate is required only to have received the highest number of votes in his or her favour. This results in the alternative name sometimes being "farthest past the post".
(src: https://en.wikipedia.org/wiki/Plurality_voting_system#First_past_the_post)
In horse racing:
post - 1) Starting point for a race. 2) An abbreviated version of post position. For example, "He drew post four." 3) As a verb, to record a win. For example, "He's posted 10 wins in 14 starts." (src: http://www.equibase.com/newfan/glossary-full.cfm#p)
I did some of my own research, and found the phrase "First Past The Post" is profoundly ill-suited to describe the voting system it's associated with.
Additionally, one writer argues that even in horse racing, the phrase should be "first on the post," as the race is over once the lead horse's nose crosses the wire, not once it's completely past. Thus all four words in the phrase are subject to question.
I agree that it is a confusing analogy. This is my understanding of it:
Normally, in a horse race, there are many rules that the jockeys must follow. The adjudicators may hold a (quick!) investigation, called a Stewards' Enquiry into any claims of that rules have been broken, and decide to disqualify a horse, or to adjust the rankings based on some penalty for failing to follow the rules.
In First Past The Post rules, however, there is an agreement between the bettors that they will disregard the stewards' tweaks, and instead base the decision "purely" on which horse passes the winning post first.
Many voting systems, such as Single Transferrable Vote, involve finding a provisional ranking of several candidates, eliminating a losing candidate, and transferring the losing votes to the next preference, which changes the rankings. The candidate with the most primary votes may not be the final winner.
By analogy, this is like the horses being re-ranked by the stewards. [Not for infringing any rules, I should add.]
However, First Past The Post voting systems have no such ranking adjustments. It is the least complicated system - the most primary votes - just like least complicated system in horse racing - the first horse to reach the finish line.
