Dominus was built by an alien race in order to dominate planets throughout space. Lucifer was sent by these aliens to Earth to dominate humanity, but Professor X and the X-Men managed to defeat him and destroy the robots that are needed to operate Dominus. Before that battle, the Supreme One banished Lucifer and call Dominus back to its planet, whatever it was.
The actual form of Dominus is that of an immense computer complex. Said computer is sentient. Its primary function is to mentally enslave the entire population of a planet, taking away their capacity for independent will. Dominus was eventually able to become independent of its creators, the Quist, and actually enslaved them as well. It gained the ability to project its conciousness into a humanoid body, effectively possessing an unnamed male Quist. It has been able to genetically engineer sentiet lifeforms out of rocks (Butte), cacti (Cactus) and desert animals (Gila). It has also been able to create and/or use highly advanced technology.