What does 'Wait This Game' do?

I was wondering what the 'Wait this game' and 'Wait any game' options do? I'm struggling to find this in the FAQ.

@Nick812

The browser will refresh when a move is available in the current game / any game.

Since this feature was added initially, browser support of OS level notifications has changed considerably, so this will be getting replaced soon so your OS will alert you the game is waiting instead of current behaviour. (If you permit RHP to send the notification, of course.)