In the comics, John Grayson and his wife were performers in Haley's Circus with their son, Dick Grayson, while preparing for a performance, Dick overhears Anthony "Boss" Zucco, a well-known and feared crime-lord, threaten the performers unless the circus' owner pays extortion money. The owner refuses, and that night young Grayson watches in horror as his parents' high wire snaps, sending them hurtling to their deaths, all while many of Gotham's elite watched on. Dick felt responsible, because he hadn't warned his parents in time.
Shortly after the tragedy, the millionaire philanthropist Bruce Wayne rescued Dick from an uncaring juvenile services system. Frustrated by the lack of attention from his new guardian and the mystery still surrounding his parents' death, Grayson sneaks out of Wayne Manor one evening to solve the crime on his own - only to stumble into Batman, who is also investigating the murder. They succeed in revealing Zucco's complicity, but he seemingly dies of a heart attack before his arrest (it was later revealed that he was still alive, but had been confined to a ventilator for decades.) Seeing a reflection of himself in Dick, Batman not only reveals his identity as Bruce Wayne to the boy, but also makes the young orphan the offer of a lifetime: the chance to become his crime-fighting partner. Dick chooses the name Robin, and his training begins.
In other media
In Batman Forever, Dick's dad appears along with his wife and son Mitchell (created for the film). They are The Flying Graysons and try to stop Two-Face from blowing up the Circus. He died along with his wife and Mitchell, leaving Dick on his own.