Dota 2 is the sequel to the popular Warcraft 3 mod known as dotA or Defense of the Ancients. Basically you pick a "hero" (a single unit you control throughout the game). Your hero will have it's own 4 skills that you will use on the opposing heroes to kill them. The aim is to destroy the enemies "Ancient" which is located at the center of their base. To get to this ancient you must destroy 2 outer towers in each lane as well as the base towers that protect the barracks, followed finally by the ancients own set of towers or turrets if you will.
(http://dota2.cyborgmatt.com/DotA2_6.73Minimap.jpg)That is the mini map of Dota 2 and as you can see there are 3 lanes, in each lane waves of 4-5 units (or creeps as they're known) spawn at intervals of 30 seconds, you can last hit these creeps to receive anywhere from 38-50 gold from killing them. You can use this gold to purchase items that will help your hero and your team in winning the game. There are 5 players per team and currently approximately 70 heroes that you can choose from, each as unique and challenging as the other.
Hope this explains, if not then go watch a youtube clip!