(covers information from several alternate timelines)
Energy transference was the process by which it was speculated Krall's life-extending technology functioned.
Having crashed on the surface of the planet Altamid in the 2160s, the USS Franklin's captain Balthazar Edison and his surviving crew mates utilized technology left on the planet by its original inhabitants to extend their lives beyond normal human lifespans. Waylaying orbiting ships and capturing members of their crew, Edison, Anderson Le, and Jessica Wolff used this energy transference technology to drain the life from their victims, sustaining their own life functions and adopting the combined biological traits of whatever species they were draining. They renamed themselves Krall, Manas and Kalara, respectively. Both Krall and Manas routinely wore mechanical suits with this technology built into them.
A century later, Krall, Manas and Kalara were no longer recognizably human, no longer even speaking in their native English. Luring the Federation starship USS Enterprise to Altamid in 2263, Krall used this energy transference on several human members of its crew, slowly restoring his Terran physiology. By the time of Krall's death, he had regained almost all of his human appearance after draining the life of five Enterprise crewmembers. However, he still retained a few non-human features. (Star Trek Beyond)
According to Star Trek: Boldly Go, Issue 5, this process drained a subject's life-force in order to prolong Krall's and Manas's life.