You were a patient at Arkham Asylum. One day, a riot happened and you had the chance to escape. Instead, you chose to help Batman and the guards. When you wake up the next day, Batman is in your room with an offer.

Your reason for being in Arkham is left vague, as in you could have actually been in there to get help or you were put there to shut you up. But bottom line, Batman saw you risk your chance at freedom to help him, and he decided to give you a chance. You're basically a Robin or Batgirl, without being full on Robin/Batgirl. There is a chance Batman will kick you out of the Batfamily if you mess up. Examples: if you constantly act reckless or endanger people to get the job done. Do well, though, and you'll just be treated as part of the batfamily (eventually).