Tough to describe. Basically, you get a Hero, buy various items for him, and try to take out the opposing team's base. Each Hero has 4 skills, including an "ultimate" which is usually a very powerful spell capable of doing massive damage. Teams are between 2-5 Heroes for each side. The ultimate goal is to destroy the opposing team's base, which is protected by a computer controlled army and powerful "towers" at various points in the map, which have to be destroyed in order to reach the base.
The heroes are really what make the game fun. Some are pushers - heroes adept at taking out towers and the enemy army, but not so good at fighting other heroes. Others are hero killers. As the game progresses, certain heroes gain strength and others lose strength. For example, magic heroes are typically at their strongest in the mid game, while physical heroes are weak early on, but very powerful late game.
This description didn't really do it justice, but it's the best I can do. For more information, check out
http://www.dota-allstars.com