A powerful military man of the Fire Nation, he has his own harbor with hundreds of firebender warships at his command. During the two years that Prince Zuko was at sea, Zhao was promoted from Captain to Commander. And then in episode 13, which takes place a few months after Zuko found out about Zhao's promotion, he was promoted again to Admiral.
Like Prince Zuko, Admiral Zhao is also hunting for the Avatar. Although this search is sometimes scoffed at by other high-ranking military men, like Colonel Shinu, who are fighting the "real war", such comments are quickly overlooked. With Zhao's powerful army backing him up, along with his vast resources and apparent confidence from the Fire Lord, Zhao is in an incredible position. Combine that with his sharp-witted mind and experienced firebending skills, and you've got quite the strong threat, both to Aang and Prince Zuko's plan to regain his honor. Zhao has already captured Aang once with the help from the YuuYan archers, so it's only a matter of time before he has the opportunity to do it again.
Zhao learned his firebending skills from the master firebender and then-Admiral, Jeong Jeong. However, this pupil and master couldn't be more different. Zhao only cared about the power that firebending would give him; the ability to destroy his enemies and wipe out the obstacles in his path. Where as Jeong Jeong was more concerned about teaching discipline, and how to keep that power under control. Although it's unknown how long Zhao stayed as his pupil, if Zhao stayed until he "got bored", chances are it wasn't very long. ^^;
Other than that, not much else is known about Zhao and his past. However it's clear that he and Prince Zuko are rivals for catching the Avatar, and have issues that go back before Zuko was banished. Zhao is also ruthless and driven to succeed, is a sore loser, and will do whatever it takes to get the job done. Results are important to him, and failure is never an option. He doesn't seem to be the type who'd let his conscience get in the way of his line of duty, and is very confident in himself. He's also been seen to become blinded by his rage, which usually leads to him making very stupid mistakes.
Zhao is constantly on the move, especially now that he is trying to capture the Avatar. So far he has been seen in his harbor, guarding the southeastern Fire Nation ocean borders, in a Fire Nation fortress and a Fire Nation city both situated in the northern areas of the Earth Kingdom.