We use an elections system calling the Single Transferable Vote (STV), a proportional system that aims to minimise 'wasted votes' - meaning yours is more likely to count.
Here's an example to explain how it works:
Imagine your friend's going to buy their lunch from a shop and they ask you if you'd like anything. You fancy some paprika crisps, but if they haven't got any you'll have ready salted, and if they have neither flavour just to get anything. So paprika's your first preference, ready salted is your second preference and after that you don't want any crisps at all because you don't like any other flavours.
This is essentially how the STV system works, you select your first preference, but should that option be eliminated your second preference will come into play and so on until you either don't mind what flavour you get (No Further Preferences), or if you don't want any of the remaining crisp options at all, you can vote to Re-Open Nominations (RON) - when you don't want any of the crisps/candidates.
In the elections the preferences come into play during each round of vote calculation. All votes are counted and if no one reaches a majority, the candidate who has received the least votes is eliminated. Anyone who had voted for this candidate as their first preference now has their second preference vote allocated to their second preference candidate and the process then repeats until someone has the majority - and wins.
So in a nutshell, you allocate your preferences to candidates until you are either indifferent to the remaining candidates (No Further Preferences) or you do not believe any of the remaining candidates are suitable for the post (Re-Open Nominations).