We use the Single Transferable Vote system (STV) - What does this mean? 

This is a preference voting system in which voters rank candidates in order of preference. The single vote can be transferred from one candidate to another according to the voters' rankings, depending on the cumulative result of other voters' ballots.

For example, on the ballot form you have 3 names:

What you do is rank these candidates in order of preferance, so if you want Peter Pan to win, the form may read:

 What is "Re-Open Nominations"?

Re-open nominations is when you feel that any of the candidates aren't suitable, so in this case you'd put a 1 in that box.