Jason is the son of Catherine and Willis Todd, and he was raised in Crime Alley. Willis was awful, and didn't return to the family after his prison sentence. It is later descovered that he was killed by Two-Face. His mom was kind, but addicted to drugs, and died of an overdose. Jason survived by himslef until he was caught stealing the tires off the Batmobile (at age 11) for money. Batman took Jason home, adopted him, and he became the next Robin at 12. Though he grew up in a tough area, Jason was a sweet kid who wanted to help people.
Jason and Batman worked well together, and Jason was a bright hope to Batman. When Jason was about 16, he finds out Catherine wasn't his birth mother. He tracks Sheila (his bio mom) down, and goes to Ethiopia alone to meet her. But it turns out that Sheila was working for the Joker, and betrays Jason. The Joker tortures Jason, and leaves him and his mom in a warehouse with bombs. Though Jason tries to save himself and his mom, the warhouse explodes and he dies.
Jason comes back from the dead years later at about 18 years old. He digs himself out of his own grave, but his mind doesn't seem to really be there. Eventually, the League of Assassins find him, and put him in the Lazarus Pit, where he is fully revived, but also more violent. He's trained by the League, and told that Batman not only didn't kill the Joker, but replaced him. He returns to Gotham, and fights Tim (his replacemnt) in Titans Tower. He become a crime lord, kills a lot of bad people, and creates a new identiy, the Red Hood. He confronts Batman about not killing the Joker, and tries to make him choose between him and the Joker. Batman chooses to save the Joker, and he and Jason don't get along for years.
Over the years, Jason becomes a bit less violent and starts to work with Batman and the Robins. He joins a team called the Outlaws, and he protects Crime Alley. He spends his time fighting crime, and occasionally interacting with his family.