The Regeneration unit (also referred to as the Regeneration tank and Regen Disc by Thorne and Starkey respectively) was a component of K9 Mark I that enabled him to rebuild his body after death, an act that could also scramble his memdrive. Seeing as at least Mark III was not fitted with a regeneration unit, it is possible he was fitted with one on Gallifrey.
After self-destructing to defeat four Jixen warriors, Starkey retrieved it and K9 regenerated into a new body. Following regeneration, K9 remembered his name but couldn't recall additional details of his past; memories of his adventures with the Doctor and Leela, his two former masters, appeared to have been at least temporarily forgotten. (K9TV: Regeneration)
Thorne and Lomax knew of the Regeneration unit and decided to acquire it. After Thorne's failed plot to cause K9 to regenerating with the use of a suicide bomber. (K9TV: Robot Gladiators) They eventually succeeded, Thorne came to Darius Pike with a proposal. Not giving the requested component's name and simply calling it "the cybernetic equivalent of an appendix". He had him try to convince K9 to agree in giving Thorne the unit in return for his missing memory chip, he promised Darius that his father Harry Pike of The Last Precinct would be released from his imprisonment if he complied. K9 feared it was a trick, although he couldn't resist the oppurtinity to discover his lost memories and accepted although it turned out to be a trick. Thorne later gave the unit to an unknown force. (K9TV: Hound of the Korven)
The unit was contained inside the Trojan, a behemoth created by mixing together DNA from aliens encountered by K9. After K9 sacrificed himself to defeat the Trojan, without his regeneration unit he seemed to be no more. However it homed back to him, allowing him to regenerate into K9 Mark 3. (K9TV: Eclipse of the Korven)