Why is Captain Jack Harkness immortal?

Answer 1

Because when the Doctor's companion (Rose) was full the time vortex energy from the Tardis, she willed him back to life, and it was so powerful that he couldn't die. Although, in other episodes it is suggested that he is the Face of Bo, and that the Face of Bo could possibly have died... eventually, after millions of years.

Watch Doctor Who episode Utopia, it explains it.

This is partially correct.... as he has stated above, it is explained by the doctor in the Doctor Who episode "Utopia".

In the 2005 Doctor Who series finale "the parting of ways", What happens is Jack is killed by the daleks and then Rose (the ninth & tenth doctors companion) absorbs the time vortex and is gifted with goddess like powers and becomes the entity BADWOLF. With these powers rose brings jack back to life. The Doctor later reveals in the episode "utopia" that she couldn't control it and made him a fixed point in time (also thought of as immortal). Though, at the end of "the last of the timelords", when jack states that he was called the face of boe back on the Boeshang Peninsula (because he was the first ever time agent), People have speculated that the doctor was wrong and The BADWOLF entity actually intended for jack to survive for another 5 billion years so that he would be able to tell the doctor that "he was not alone" and would be partially ready for the MASTER's return in the 2007 3-part series finale.