In the comics, John Grayson and his wife Mary 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 billionare 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.
New 52 (Prime Earth)
In the New 52, it would be revealed that John was the grandson of William Cobb, the chief Talon for the Court of Owls. He himself was the son of William's son who was known as, "The Gray Son of Gotham", giving the family their surname.
Due to this position, John would aid the Court of Owls in training young would-be-Talons for their ranks. This was the intention of Haly's Circus which was owned by the Court, acting as a facade for the Court to train individuals in acts such as acrobatics, knife-throwing, contortion, etc.
At some point, John fell in-love with one Mary Grayson despite her close childhood friend Dick hating him. The two would have a child together who they named after Dick though the family-friend would come to seemingly leave their life as he was in-love with Mary. John would go on to begin to groom Dick to be a member of the Court of Owls without his knowing.
Eventually, John and Mary were both killed by the gangster Tony Zucco and their son would be adopted by Bruce Wayne where he'd use his assassin's training for good rather than for the Court.
In other media
See Mr. Grayson