Biography
The man who came to be known as Captain Jack Harkness worked as a Time Agent until he discovered that the Agency had erased two years of his memory. After leaving the agency, he worked as a conman, finding pieces of space junk and directing them to soon-to-be disaster sites, selling them to passers by, and letting them get destroyed before the buyers could pick up their merchandise. At some point during his time as a conman, Jack took the name of a Captain who died in the Second World War. "Jack" would later meet his namesake during a trip back in time, and would develop a short-lived relationship with him.
While pulling a con with a Chula Ambulance during the London Blitz, he spotted Rose Tyler hanging from a barrage balloon. He rescued Rose, who introduced him to the Ninth Doctor. After sacrificing himself to help clean up after the damage done by the Chula Ambulance's nano-genes, he was rescued by the Doctor and Rose. He accompanied them on their subsequent adventures. He was aboard Satellite 5 when the Daleks launched their assault on Earth, and was exterminated while defending the satellite from their advance. He was resurrected by Rose Tyler, who briefly gained the power of the Time Lords by looking into the Time Vortex. Returned to life, Jack found he had been rendered immortal, although he was unable to rejoin the Doctor and Rose before the TARDIS departed, and was left stranded on the satellite.
Torchwood
Following the last battle of the Time War on Satellite 5, Jack began the process of "rebuilding the Earth" according to the newly-regenerated Tenth Doctor. He was able to escape the satellite, and ultimately joined the Torchwood Institute after falling through a rift in time. He became the leader of Torchwood 3, based under the Cardiff rift. Jack held on to the hope of re-establishing contact with the Doctor, whom Jack believed was the only being who could help him deal with, and perhaps negate the effects of, his newfound immortality.
After the rift was finally opened by Owen Harper, Jack was forced to confront Abbadon, released from the rift by Bilis Manger. The beast was destroyed while attempting to leech Jack's life, though the exertion rendered Jack dead for three days, his immortality apparently unable to save him. He was brought back to life by a kiss from Gwen Cooper, to whom he later confided that there had been "nothing" after death.
Shortly after his resurrection, Jack noticed the Tenth Doctor's hand begin to glow within its hyperbaric chamber, and witnessed the materialization of the TARDIS in the Hub. The Torchwood team arrived to find the Hub empty, Jack presumably having left with the Doctor.
Behind the Scenes
Jack Harkness' first name was originally "Jax".