After you defeat The Illidari Council in The Black Temple, you will soon find out that there is a big door that prevents you from progressing further into the raid and fight the final boss, Illidan Stormrage himself. However, it's quite easy to open this door, and what you need to do is head down to the room where you fought with The Illidari Council. At this point Akama should have arrived there, and speak with him. He gives you a dialogue option to ask for his help, so do this. He will now run up the stairs and open the door for you (after a bit of RP).
And that's it! The door is open, and you are ready to fight Illidan.