The White God was a relic of the Time Lords left on the planet Lethe, captured by the pirate ship Parliament of Rats, and worshiped by the sailors as a sea deity.
When Brunner, a priest-physician, joined the Lung of Heaven to find the White God and expose it as a false god, the Lung was attacked by the Parliament and Brunner was taken aboard with Nyssa. They were imprisoned in a room with a mirror. The White God then appeared out of the mirror and Brunner unsuccessfully tried to defeat it. At this time, Nyssa theorised that it was a white hole.
After Constantine and the Fifth Doctor rescued Brunner and Nyssa, the Doctor was able to communicate with the entity through Brunner's staff and order it to destroy itself. In doing so, it caused the Parliament to break apart and sink.
Back aboard the Lung, the Doctor learned that Constantine had created the White God for her amusement. (PROSE: The Parliament of Rats)