In Multiplay you can play in Leagues, Custom Games, and Cooperative Games.
In the Leagues you play against random people in your area that are around your level. You compete in normal gameplay to beat the other person. The more wins you get, the more points, the more points the more likely you will move up into higher leagues.
The League ranks go in the following order.
There are different types of leagues as well.
I am currently in Bronze 1v1, Gold 2v2, and Platinum 4v4, also im Platinum for 2v2 with my friends.
The Custom game area of the multiplay is composed of several Blizzard made games and lots of player made games.
Blizzard came out recently with 3 custom games that they also made achievements for. These three are:
In StarJeweled you match 3 of a kind to clear them and get points, it is similar to Bejeweled. Also you must use those points to buy troops to fight the enemy.
In Left2Die two players build up defenses and try to survive for as long as they can against a zerg horde.
In AiurChef a large group of players compete to find the most ingredients on the map to create recipies.