Barbara Gordon's Origin
The first wife of Gotham City police commissioner James W. Gordon and the mother of James Gordon, Jr., little is known of Barbara's early life. Barbara and James (then a police lieutenant) moved to Gotham from Chicago, Illinois, shortly before the couple discovered that they were expecting their first child. A short time later, Lt. Gordon was assigned to track down the mysterious "Batman". After James, Jr. was born, Barbara discovered that her husband was having an affair with his partner, Sarah Essen. This and other tensions in their marriage eventually led Barbara to divorce her husband.
At some point after the events of Year One, Jim and Barbara took in and adopted their niece Barbara, whose parents had died in a car accident. However, some time after, the older Barbara divorced Jim, and took their son with her to Chicago while the younger Barbara stayed with Jim.
At times it was implied and shown that Babara was killed during a car accident, and references to James Jr. were rarely mentioned. However, it was later retconned that Barbara and James Jr. were indeed alive, but that James Jr. has shown sociopath behavior. Over the years, Barbara (with occasional help from her ex-husband and his second wife Sarah Essen), attempted to get James Jr. help, once even having him institutionalized in Arkham.
James Jr. would eventually target his father, his sister and his mother, even attacking Barbara and making it look like the Joker had been responsible. She survived the attack, but was left traumatized by the experience.
Following the Flashpoint continuity changes to the DC Universe that brought about The New 52, Barbara mentions to her new roommate, Alysia Yeoh, that instead of dying or divorcing Jim Gordon properly, her mother walked out on her, James Jr. and her father Jim Sr. On Christmas morning, when Barbara and Alysia are opening presents, the doorbell rings, and Barbara finds her mother waiting for her outside.
It was revealed that Barbara had left her family because of her son James' sociopathic behavior. James Jr. one day threatened to kill Barbara Jr. if Barbara Sr. did not leave the family. Fearing for the safety of her family, and due to her own emotional weakness, she abruptly abandoned the family in the hopes it would spare the life of her daughter. While Babs understood how dangerous, it was difficult for her to trust her mother.
Barbara Sr. was later kidnapped by the Joker, who had supposedly figured out the secret identities of the entire Bat-family, and used Batgirl's mother as blackmail to force Batgirl into marriage with him, going so far as to cutting off Barbara Sr.'s finger. Batgirl was able to save her mother, but the family would again be targeted by James Jr. who intended to make good on his promise to his mother that he would kill Barbara if she returned.
In other media
Batman: Year One (2011)
In the animated adaptation of the second part of Batman: The Dark Knight Returns, Barbara makes a subtle cameo in a framed picture in Gordon's home, along with an adolescent James Gordon, Jr. Likely a production Easter egg, her appearance and design matches the one used in Batman: Year One.
Barbara Kean appears in the television series Gotham, which acts as an origin show to several DC related characters in the years prior to Bruce Wayne becoming Batman. She is introduced in the "Pilot" episode, initially as the fiancée to protagonist James Gordon. But it becomes clear she has had a troubled past with alcohol and drugs, and is also revealed as the former bisexual partner of Renee Montoya.
Unlike the comic counterpart, this version later becomes a villain in the show. In fact, after being mentally abused by the Ogre, she murders her parents near the end of the first season and tries to kill Gordon's new partner, Leslie Thompkins.
In the second season she becomes a part of a group known as 'The Maniax' and works under the season's primary antagonist, Theo Galavan. She then tries to kill herself but ending up in a coma instead, she later wakes up and helps Jim with the intention of reconciling with him, failing.
In the third season she continues her career as a gangster along with her girlfriend Tabitha Galavan and Butch Gilzean (later known as Solomon Grundy). She then allies with Edward Nygma with the intention of stopping Oswald Cobblepot from beign the king of the city. She briefly becomes the queen of Gotham before being electrocuted to death by Tabitha.
In the fourth season Barbara gets resurrected by Ra's al Ghul. She then makes peace and reunites with Tabitha and Selina Kyle, being known as The Sirens. They briefly work with Sofia Falcone and they stop Penguin‘s control over the city. Ra's then makes her the new Demon’s Head, which leads her to summon the League of Shadows, she eventually gives up her powers to save Tabitha. The two, with the help of the Sisters of the League, claim their territory in “The Sirens Club” when villains take control over Gotham City.
The first appearance of James Gordon's wife was in World's Finest #53. She was not given the name "Barbara" until 1981, after Barbara Gordon had become an established character. She was reintroduced Post-Crisis in Batman: Year One.