Doctor Who's resurgence in 2005 regenerated the fandom to a scale unlike any other. The first series introduced audiences to the 9th Doctor, as well as many other staples from the series prior, like its campy villains and memorable companions. Perhaps the most important one introduced in this run is Captain Jack Harkness, a member of the Time Agency who eventually becomes a recurring companion for the 9th and 10th Doctors. He'll also return to accompany the 13th Doctor for the holiday special. Captain Jack Harkness has been able to return to the series so often due to his immortality, which he gained at the end of the first season.
During "The Parting Ways," the 9th Doctor, Rose Tyler and Captain Jack Harkness find themselves on a satellite orbiting space that broadcasts ten thousand channels of reality TV programming to Earth. All is well until the satellite is invaded by the Daleks. The team attempts to ward off the Daleks with the help of some of the contestants, but it hits a point where The Doctor has to launch a Delta Wave that fries all life within the area, Daleks and humans alike. The Doctor also sends Rose Tyler back to the modern day in order to save her.
Rose attempts to get back to The Doctor in order to help save him, so she breaks open a panel on the TARDIS, which contains its heart. She absorbs all the energy of the heart and makes her way back to The Doctor, with a god-like presence to her.
It is revealed that the heart of the TARDIS is the time vortex, which allows the TARDIS the ability to traverse space and time. While all this is going on, the contestants and Captain Jack are attempting to ward off the Daleks. They all get exterminated, including Captain Jack. Rose arrives at the satellite and uses her new god-like powers to turn the Daleks into dust and reanimate Captain Jack.
Captain Jack awakens from his death; however, The Doctor and Rose left in the TARDIS, abandoning him. He uses his vortex manipulator to return to present day Earth, hoping to run into The Doctor at some point in time. However, he finds himself in 1869 and has to wait for The Doctor. During this time, Jack discovers him immortality, and while he can suffer fatal injuries, his body regenerates itself, so he cannot die.
Through his immortality, he traverses the cosmos and eventually reopens Torchwood as a smaller organization, and his adventures are documented in the short lived spin-off, Torchwood. Audiences come to find out where Jack's life ends, as he reveals in Season 3, Episode 13, "Last of the Time Lords," that his nickname as a child was The Face of Boe. Earlier on, fans met The Face of Boe, who died in Season 3, Episode 3 "Gridlock," proving that there is one way to bring an end to Captain Jack.