what is bonus? and 15 || 10

Hello? What is "bonus" parameter?

Also, what does it means 15 ||  10

should I understand 15 minutes game (and what is 10 then?)

"Bonus" is the amount of bonus time that each player gets every move.  In 15|10 games, for example, each player gets 15 minutes and an additional 10 seconds every time they make a move.

What's the point of that? Moving faster is better in time terms?

The point of bonus time and time delay (the clock doesn't start counting down until some time has passed) is that it gives a greater opportunity for games to be decided on the board rather than by the clock.  So long as you can move within the bonus/delay, you won't lose on time.

And yes, if you move quickly enough with bonus time, you can regain some of the time you used up during the times when you needed to think a little more.  It allows for more flexible time management - again, so that the game can be decided by gameplay and not the clock.