Voters in the UK are used to placing a single cross next to the candidate they want. That works well if you just want to see which of two candidates will win, but begins to get tricky when there’s more than two candidates: you’ll often see the problems of minority election.
In many systems, especially proportional ones, instead voters choose which order they’d like to support the candidates in, often by writing “1″, “2″, “3″, etc., although there are other ways to design the ballot paper.
So, instead of:
I prefer candidate C
voters can say:
I prefer candidate C, but failing that,
I prefer candidate A, and failing that,
until they run out of options, or choose to stop voting.
AV is one type of preferential voting, but there are many others.