The Repulsion was an entity that inhabited a dimension "between death and life" in a pocket dimension that acted as his domain. The Fourth Doctor theorised it could have been a creature that was banished from the outer dimensions and was an "evil before time".
The creature was known to the Arboretans, who described it as "unfettered evil". Despite this, its actual realm was relatively peaceful, shaping itself to the perceptions of each individual visitor to give them their own vision of an afterlife.
The Repulsion used the time distortion created by the Necroport to gain access to the real world. Needing physical form, it took the survivors of the Cerberus from 2815 and sent them to the year 3012 via its own dimension; it replaced the zombies it created from the last trip of the Beautiful Death (which it hijacked) in the year 3012 with the passengers' essence so that the 'zombies' could act as vessels for its life force (the only one to escape this fate was Hoopy, whose chosen spirit chose to remain in the Repulsion's realm). It was only able to control the zombies by remote control, whereas the possessed passengers contained actual elements of its consciousness. Being possessed by the Repulsion resulted in black oily slime filling the mouths and eyes of its victims.
When the Repulsion tried to possess the Doctor after he was connected to the Necroport to enter its realm, he tricked it into possessing K9 by connecting him to the Necroport instead. The Doctor then downloaded the creature into the mind of the suicidally depressed computer ERIC, on the G-Lock. The Doctor then helped ERIC to die by reconfiguring his circuitry to trigger an overload, thus destroying the Repulsion. (PROSE: Festival of Death)