The White God was a living white hole pulled from the pre-universe by the staff. On the planet Lethe, where it was kept on the Parliament of Rats, it was worshipped as a sea deity in opposition to Om, so Brunner set out on the Lung of Heaven to kill it.
When the Lung was attacked by the Parliament, Brunner and Nyssa were taken aboard and imprisoned in a room with a mirror. The White God then appeared out of the mirror and Brunner unsuccessfully tried to defeat it.
After Constantine and the Fifth Doctor rescued Brunner and Nyssa, the Doctor ordered the staff to destroy itself; as it did so, the White God split open and the Parliament broke apart and sank.
Back aboard the Lung, the Doctor learned that Constantine had created the White God to satisfy the wishes of Brunner and Korzen. (PROSE: The Parliament of Rats)