First past the post - the party with the most votes ‘wins’. It’s in contrast to a range of other systems that rely on proportionality or preferential voting to ensure that the party or parties with majority support wins.
For example, imagine a scenario where there are 10 constituencies electing a representative by FPTP. In each of those 10 constituencies, the result is identical as follows:
- Nazi - 40%
- Liberal - 30%
- Socialist - 20%
- Conservative - 10%
Under FPTP, the Nazi would be the top candidate in every constituency, and so win 10 out of 10 seats and have total control of the legislature, even though 60% of people voted anti-Nazi. This is the system in the UK and US.
Under a proportional system, you would allocate the seats in proportion to the votes cast - so 4 for the Nazis, 3 for the Liberals, 2 for the Socialists and 1 for the Conservatives. The non-Nazis would then have a legislative majority (6 out of 10 seats) that reflects how people actually voted, and could form an anti-Nazi coalition government. This is the system in the Netherlands or Germany for example.
Under a preferential system, you still elect seats on a constituency basis, but you make sure that the winning candidate is preferred by a majority of voters in the constituency - either by having multi-round elections or by having voters rank candidates instead of just voting for one. In a simplified system, you could rule out all but the top two candidates (in this case, Nazi and Liberal), and then have a second round of votes two weeks later for voters to decide between those two candidates to represent their seat. This tends to favour more moderate candidates so it’s likely under such a system that the Liberal would generally defeat the Nazi in the second round in most seats. This is the system in France.
There are also hybrid systems like Single Transferrable Vote, which simultaneously achieve proportionality and preferential voting - this is used in Ireland.
That is exactly how the US system works, with a handful of exceptions.
For the election of a Senator or Representative - it’s almost always FPTP. The candidate that gets the most votes wins the seat, regardless of whether or not they got a majority of the vote. The state of Georgia is an example of an exception, as they hold a runoff election for Senator if the leading candidate falls short of 50% - as happened with the elections of Jon Ossoff and Raphael Warnock, both of which went to runoff.
For the presidential election, this also how it works in the vast majority of cases. 100% of a state’s electoral college vote goes to the candidate that gets the most votes, regardless of whether or not they got a majority of the votes in the state. You have a situations like Texas in 2020 giving 38 electoral college votes to Trump and zero to Biden (versus a proportional allocation of more like 20 Trump, 17 Biden and 1 Jorgensen). That electoral college system results in situations like 1992, when Bill Clinton got a 370 vote electoral college landslide on 43% of the vote because of Ross Perot’s third-party candidacy, as well as situations like 2000 and 2016 where a Republican candidate who came 2nd in the national vote still came 1st in the electoral college by virtue of coming first past the post in enough individual states. (I believe the exceptions are Nebraska and Maine, which split their electoral college votes.)