From the Leaverbuster FAQ:
WHAT IS LEAVERBUSTER?
LeaverBuster is a system we have implemented in order to discourage Summoners from repeatedly leaving matches and/or idling during gameplay. Summoners who exhibit this behavior and have a trend of leaving/idling in games will be placed in a low priority queue.
HOW LONG WILL I REMAIN IN THE LOW PRIORITY QUEUE?
You will be placed in the low priority queue for 5 games. If you continuously leave, the low priority queue timers increase from 5 minutes per game to 20 minutes per game.
I'M A PAYING USER. SHOULDN'T I GET A BIT OF LENIENCY ON THIS?
No. Every Summoner contributes to their team's victory or defeat on the Fields of Justice. Those who repeatedly leave games or idle during gameplay hurt their team and the overall experience of all Summoners on the field. In order to discourage this behavior, we must take action against those who make it a habit.
IT'S NOT MY FAULT. MY INTERNET/YOUR SERVERS DISCONNECTED ME. I HAD A REAL-LIFE EMERGENCY. I HAD TO GET OFF THE COMPUTER. THE GAME CRASHED. UNBAN ME!
We understand that players may be forced to leave from time to time so the system has been designed to keep these situations in mind. After leaving a few games, you will be placed into a low priority queue; as long as you can complete 5 matchmade games without leaving, you will be returned to the normal queue. However, if you continue to leave games, you will remain in the low priority queue.