Actually, its a rating system ported over to gaming and almost always fails. RIOT uses a highly tweaked version of it cause it straight across was very very poor to start with.
Check out the wikipedia page if ya want to know more about Elo and the method he made, here is a quote:
The Elo rating system is a method for calculating the relative skill levels of players in two-player games such as chess. It is named after its creator Arpad Elo, a Hungarian-born American physics professor.
The Elo system was invented as an improved chess rating system, but today it is also used in many other games. It is also used as a rating system for multiplayer competition in a number of video games,1 and has been adapted to team sports including association football, American college football, basketball, and Major League Baseball.
Anywho, The name has stuck despite the rating system being tweaked and updated into its much more 50/50 win/loss ratio that the game has no a days. Overall this will not change your play style at all, it simply tries to pair you with a team that has an overall consistent ELO rating that you are about to face in the case of PvP matches. For Co-Op it matches you with people at roughly the same rating as you.