MMR also known as Match Making Rating is a hidden rating of your account what determines your position on a ranked ladder. It is your actual but hidden rating, that affect the skill of the players you play with or against and the amount of LP (League Points) that you will earn after win, or lose per defeat.
MMR is quite similar to Elo System, but Riot Games decided that Elo System is more interesting and shows the real things.
There are 7 Leagues from Bronze to the Challenger, while MMR is just a numerical number that shows your average skill. The more about MMR and Elo you could find on the Boosteria Official Website.