In short, R.O.N is your chance to express your desire not to vote for any of the candidates on offer and Re-Open Nominations. 

The Alternative Transferable Vote (ATV) is a system of preferential voting designed to minimize "wasted" votes and provide proportional representation.

To give you a bit of an introduction to how it works let's imagine a friend is going to a shop to buy their lunch and they ask you if you'd like anything. You quite fancy some crisps so reply that you'd like a bag of Salt & Vinegar, but if they haven't got any you'll have Ready Salted and if they have neither flavour just to get anything.

What you're saying is that Salt & Vinegar is your first preference, Ready Salted is your second preference and after that you don't really mind what you get - you have no further preferences. 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 (No Further Preferences) or if you do not want any of the remaining candidates you can vote to Re-Open Nominations (RON) - in our example this would be represented by not wanting any other flavours than Salt & Vinegar or Ready Salted.

In our example your preferences are used to choose which of the available flavours you would like - in the elections the preferences come into play during each round of vote calculation. All votes are counted and 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 there is a winner.

So in a nutshell you allocate your preferences to candidates until you are either indifferent to the remaining candidates (No Further Preferences or NFP) or you do not believe any of the remaining candidates are suitable for the post (Re-Open Nominations or RON)