Melody "Mels" Pond, later River Song, was a "child of the TARDIS". She was human with Time Lord DNA, conceived by her parents, Amy Pond and Rory Williams, onboard the Doctor's TARDIS as it travelled through the Time Vortex. This gave her the potential for great strength and regeneration, to pilot the TARDIS and understand complex principles of Time and Space.
Melody was stolen from her parents as an infant by Madame Kovarian to become a weapon of the Silence in their war against the Doctor. After her second regeneration, she killed the Eleventh Doctor, but then broke her mental conditioning to give her remaining regenerations to revivify his corpse.
The Doctor and her parents left her to make her own way in the universe. With no connection to her family or the Silence, River became an archaeologist, ostensibly to track the Doctor through time. She crossed the Doctor's path on several occasions, generally with the result that she was meeting him at progressively earlier point in his own time stream. Hoping to avoid temporal paradoxes, the Doctor gave her a diary to keep track of their meetings and to prevent her from revealing "spoilers" to him about his own future.
Again forced by the Silence, she made a second attempt on the Eleventh Doctor's life. Though actually unsuccessful, she was convicted of his murder and spent many years in Stormcage Containment Facility for it — apparently to convince the universe that the Doctor actually was dead. This confinement was made more bearable by escaping frequently to go on out on dates with the Doctor.
Ultimately, she died saving the life of the Tenth Doctor in the Library. That incarnation of the Doctor saved her consciousness digitally to the Library's computer system, granting her a form of theoretical immortality.