After Nightwing moved on from Gotham, Batman aimed to try and fill the void of Robin. Eventually he would meet a young man named Jason Todd, and soon took him under his wing. What he didn't realize at the time was that this partnership would be unlike any he had before...or since.
Jason was nothing like Dick Grayson, something readers were all too happy to point out. So when the time came for a dramatic shift in the Batman comics, the writers were thinking of killing off Jason. So they left it to the fans whether he should live or die.
They chose to kill him.
He was blown up by the Joker after being beaten mercilessly, and not even Batman could save him. But to Batman's surprise, Jason didn't stay dead. Via one of two means (depending on the continuity) Jason came back, but not exactly how he was before. For he came back meaner, and with a vengeance, his thoughts on crime-fighting changed. He didn't mind killing now, and dishing out the punishment he thought criminals deserved.
This mentality would lead him to clash with Batman and the family on several occassions. Eventually, he would come back to the light side...more-or-less. But everyone in the Bat-family knows that at any moment, Jason Todd can change his mind.