First past the post or plurality voting is a Democratic system and the simplest kind of voting system. Each voter votes for one candidate, and whichever candidate gets the most votes is the winner.
Compared to other systems
First past the post ia OK for two-candidate races but it is bad for more than two. That system encourages voters to vote for the lesser of the two major evils in order to keep the greater one from winning. Fear of wasting one's vote causes convergence on two-party systems, an effect called Duverger's law after Maurice Duverger, the Sociologist who noticed and described that effect.
Most alternatives to first-past-the-post are more friendly to multiple candidates and parties. The simplest of them is run-off elections. If no candidate wins a majority, then the two top candidates have another election. The President of France is elected in that fashion. Instant Run-Off Voting and Proportional representation do even better at being multiplicity-friendly.
Countries with FPTP
FPTP continues to be used in two of the oldest present-day democracies, the United States and the United Kingdom, even though many others have abandoned it for various approximations of proportional representation. The issue is, democracy doesn't really work out in either nation. The Democrats and Republicans have dominated the system since the Civil War, and the Bull Moose and Reform parties are the only two that ever even stood a chance. The UK's three-party system is even worse, where, in 2015, the Conservatives won an absolute majority with only 36.8% of the vote, and sometimes, the Liberal Democrats, who are the major third party, can manipulate other parties in their favor when they get enough seats that whichever party enters a coalition with them gets to rule.