Single Transferable Vote means that voters are able to rank candidates in order of preference, rather than simply pick their most preferred candidate.
In a STV election, candidates must reach a certain number of votes to get elected. This is called a quota. The quota is based on the total number of votes and the number of positions being filled. For example, with 1500 votes cast for a single position, the quota is 750 votes.
The following two examples demonstrate how STV works for electing a Mayor or Council/Board in New Zealand's Local Elections. If you want an even deeper understanding, check out this STV Q&A.