Maxi-chlorians were a creation of Darth Tenebrous as a way to achieve a form of eternal life. During his lifetime, Tenebrous injected himself with a retrovirus, that infected some of his midi-chlorians turning them into maxi-chlorians at the loss of his precognition abilities. These maxi-chlorians were long lived midi-chlorians that would linger after Tenebrous died, instead of migrating back into The Force.
After dying, these midi-chlorians remained, containing Tenebrous's consciousness. They flew out of his old body and into his apprentice Darth Plagueis, essentially giving Tenebrous a "host" and giving him access to his apprentice's foresight. However, after realizing Plagueis's future failure would destroy his plans, Tenebrous panicked and shot himself out of Plagueis's body where he was forced to relive his final moments and afterwards in a loop, over and over for all eternity.