In an election, a candidate has a plurality if he/she has more votes than any other candidate. This differs from a majority if there are more than two candidates involved in the election.
For example, if Candidate A has 40% of the vote, Candidate B has 35%, and Candidate C has the remaining 25% of the vote, then Candidate A has a plurality but not a majority. Thus, as theorist Donald Saari puts it, "The plurality vote is the only procedure that will elect someone who's despised by almost two-thirds of the voters."
The most commonly used alternative to a plurality vote (a.k.a. "first past the post") is a runoff election, which eliminates "extra" candidates until one is chosen by a majority.