STV is also used to elect MEPs from Ireland and Malta; all other EU member states use list system. In the UK, STV is also used in Scottish and Northern Irish local government, and to elect the Northern Ireland Assembly.
STV is a way of electing more than one candidate. Typically STV is used to elect 2-7 candidates; for larger numbers than that, it starts to get unwieldy. STV aims at electing those candidates such that all the voters’ preferences are most satisfied. Of course, it would be impossible to elect candidates that completely satisfy this criterion, without every voter being their own candidate, but STV is generally held to be the best system for electing a small number of candidates.
Because STV is slightly complicated, I'll explain it by way of explaining a similar, but simpler system first, the Alternative Vote.
The Alternative Vote -- usually abbeviated AV -- is a way of electing one candidate to a position. I said earlier that STV is for electing 2 or more candidates; that’s not quite true, STV can be used to elect one candidate, and when that is done is it called AV. AV is therefore a special case of STV when only one candidate is being elected.
That’s easy. You mark a “1″ against the candidate you most prefer, “2″ against your second favourite candidate, etc, until you have no further preferences for any of the remaining candidates.
The first preference votes for all the candidates are counted. If any candidate has over 50% of the total votes, that candidate is elected. If not, the candidate with the least number of votes is eliminated, and all those votes are redirected to their next highest preference. This continues until one candidate has more voters than all the others put to together; that candidate is then declared the winner.
STV is the same idea, except that there are multiple winners. So if the election elects N candidates, then you keep eliminating candidates (as with AV) until there at N left.
But sometimes (usually, in fact) a candidate has more than the votes they need to win. For example, consider a 4-seat election where there are 1000 total votes. Four candidates each have 201 votes. These candidates must all be elected, since all other candidates between them can only get 196 votes. 201 is therefore a “magic number” that guarantees that a candidate will be elected (it’s usually called the “quota”).
Every vote above the quota is a surplus vote that could have gone to electing someone else. And in STV, that’s what happens: if a candidate has more votes than the quota, the candidate is elected, and that fraction of each vote that is above the quote is re-allocated to the voter’s next preference. In our example, if the top candidate gets 210 votes, then 9/201 of each vote is re-allocated. STV is usually counted by computer, for speed.