Zuko

Prince Zuko is a disgraced 16-year-old prince of the Fire Nation who is in a ongoing quest to find Aang the Avatar

(Note this contains many spoilers, if you haven't seen episode 12: "The Storm" do not read any farther)

Younger years (before the hunt for the Avatar)
Zuko started off as a kind hearted child who had great ambitions to become a good leader. Zuko was very outspoken and that got him into trouble and when he was 14, Zuko was allowed to attend a war meeting in his father's war chamber. But when he spoke out in defense of a newly recruited battalion that was suggested by a general to be sacrificed as bait for the enemy, his father took the outburst as utter disrespect. The only way to resolve the issue was by an Agni Kai; and Zuko expected to fight the General who he questioned, but instead he had to fight his own father and thus got a horrible scar that stretches from his eye to the back over his ear.

Zuko today
Now at the age of 16 Zuko has been banished and is never allowed to return home unless he can fulfill a seemingly impossible mission: find and capture the Avatar. During his two years in exile, he has trained himself to become a powerful Firebender. He is focused, driven, intelligent and honorable, but he is also very bitter, Zuko is obsessed with what he believes is his destiny: capturing the Avatar, in order to redeem his honor and be accepted back by his father. Zuko is desperate to regain his throne, but also is learning that there are more important things, such as the safety of his uncle General Iroh and his crew. Zuko does not care about taking over the world, as does the fire lord, but only wants his father to love him.

Family
Outside of his Uncle and father we now know it has been confirmed that Zuko has a younger sister named Azula, as seen in the memories of a little girl running with him. She is the girl seen smiling at Zuko's punishment in the episode the storm and something must have happened betweened them because one moment they were playing so happily in one scene and yet Azula is smirking at Zuko's punishment in the same episode.

Zuko also has a strange but close paternal relationship with his uncle Iroh. Although Zuko often snaps at his uncle, and Iroh often teases Zuko, the two have a strong bond. Iroh threw Commander Zhao across a field for Zuko and the pain is evident on his face when he describes the circumstances around Zuko's banishment. Zuko is respectful of his uncle and gave up a chance to hunt for the Avatar when he needed to save his captured uncle. Although they had one major fight in Episode Twelve, Zuko apologized for his harsh words.

Personality and personal life
Prince Zuko is hotheaded, impatient, short-tempered, and determined in everything he does. He's also honorable, sees no need for unnecessary violence and killing as long as he gets what he needs. And while he's obsessed with capturing the Avatar, he's slowly realizing that there are other things more important, like the safety of his family and/or crew. He often meditates alone in his room in front of a large dragon motif; being taught by Iroh that a level head is a sign of a good leader. He has issues with Admiral Zhao and clearly dislikes him, because Zhao is competing with him to capture the Avatar. Zhao constantly refers to Zuko as a traitor and even questions his loyalty to the Fire Nation, but what caused such remarks is also unknown. In the few flashbacks shown of Zuko, it's clear that he cares for the Fire Nation and its people.

Content credit: Distant horizon