Gil Mason was a senior police officer who served as deputy police commissioner under James Gordon's command. He eventually took the job himself when Gordon was thrown into jail after being wrongly accused of taking bribes from Rupert Thorne.
Nothing is known about Gil Mason's personal or professional history prior to his taking the job as deputy police commissioner. It is implied though that he ascended to the position because of Two-Face's behind the scenes manipulation.
When he first came on the job, Mason demonstrated a high level of practical ability and Jim Gordon hailed him as a godsend and had begun to trust him. He also, during his tenure, brought down the crime boss Rupert Thorne and had other successes in dealing with the criminal rackets in Gotham; much of this was done with the help of a mysterious informant who was obviously Two-Face manipulating circumstances behind the scenes.
It seemed that he was romantically interested in Barbara Gordon and that she had begun to return those feelings until she realized that he was responsible for multiple criminal acts including framing her father. After he served Gordon with the arrest warrant and jailed him, he took over Gordon's job and appeared to be supportive of bid for bail which had been denied by the court system, even appearing at a public rally for him. At the rally, an incident was staged by Two-Face's mob that revealed Mason's true nature. Specifically, a drive by shooting occurred and Mason ducked before he saw the gun barrels; something Dick Grayson noticed on playing back the videotape of the newscast covering the event.
Barbara, who was disguised as Batman and at the event in hopes of mustering public support for her father got a good look at one of gunman before fleeing the scene. She proceeded to do some research and found the person was she looking for. She rushed to tell Mason about it only to find that same person in his apartment. Realizing the kind of person Mason really was and that there was no one she could trust; she created the identity of Batgirl and proceeded to trail the corrupt deputy commissioner to a meeting with Two-Face after spying on him from an adjoining rooftop. She followed him to the meeting in question where Mason had been called to identify a criminal named Matches Malone, who was Batman in disguise, and proceeded to get caught, but managed to escape with the help of Batman. But, after the abandoned subway station they were in got flooded, she was left on her own.
Two-Face engineered a prison break to make Gordon look guilty and eventually kill him. This way, Mason could take over the job of police commissioner permanently and help Two-Face consolidate his power over the criminal gangs in Gotham City. After saving her father while in costume on the Gotham pier overlooking the harbor, Batgirl had a final fight with Mason on a speedboat as he tried to escape. She grabbed onto the rope still tied the boat and pulled herself up onto the boat while it was moving at high speed across the water. Mason fired his weapon damaging the fuel tanks and setting fire to them. He succeeded in unmasking her and expressed surprise at her true identity but sustained injuries during the fight that put him into a coma.
Regardless of his comatose state, Mason was indicted on charges for his crimes. It is unknown if he recovered from his coma, or if he even remembers Batgirl's identity.