The Ender Sword does 7 points of damage (equivalent to 3.5 hearts) which makes it equal to a Diamond Sword. It also has the same durability as one.
The Ender Sword has two main abilities, with the first being that when you block with it you are immune to incoming damage. The second ability is if you shift-right click you will teleport a short distance taking a small amount of the durabilty of the sword. This ablity is able to teleport you through (and into) walls allowing you to skip traps and puzzles in dungeons and have a quick escape if you are trapped somewhere.