The bonus time is time added to your time after you make each move.
What does bonus time mean in live chess?

You will see time set like 15-0 meaning its a 15 minute game, if you see like 10-10 or 15-15, it a fifteen minute game with 15 minutes bonus time. Once you make a move some time is added to you game. It makes it a 30 minute maximum if it adds it all. The computer figures and adds it. I really dont know how it does it...

This helped me understand quite a bit: http://blog.chess.com/DrawMaster/how-to-calculate-the-effect-of-bonus-time

You will see time set like 15-0 meaning its a 15 minute game, if you see like 10-10 or 15-15, it a fifteen minute game with 15 minutes bonus time. Once you make a move some time is added to you game. It makes it a 30 minute maximum if it adds it all. The computer figures and adds it. I really dont know how it does it...
Thank you for explaining :)

Why not call it a thirty minute game then?
15-15 would mean you get 15 minutes on the clock at the start, but for every move you make you get a bonus 15 SECONDS.
The aim of this kind of time control is that you will always have at least 15 seconds to make a move.

bonus time will be added if your move is strong enough..the main idea of this practice is if you are in a wining position...and u have lesser time than your opponent.then u don't have to lose on time..computer will add time(2 sec/move in 5/2 game) as bonus...but remember computer will not add time in every move..
The computer on a chess site (I am not referring to dedicated chess engines, of course) can't tell a good move from a bad one.
What does the bonus time mean; how is it figured? How is this bonus enabled?