After the three Ages of Darkness (Ultima 1, Ultima 2 and Ultima 3), the lands of Sosaria were unified by the good Lord British. The newborn kingdom was named Britannia. The people still lacked direction, though, therefore Lord British proclaimed the Quest of the Avatar (Ultima 4) to promote eight Virtues. The champion who managed to complete the Quest was called Avatar.
After the Quest of the Avatar more earthquakes happened, and the bottom of the dungeons opened to reveal an unexplored underworld. Lord British himself started a journey to explore the underworld with a group of loyal knights. Before leaving, he appointed the trusted Lord Blackthorn as regent of the kingdom.
When Lord British and his knights got to the underworld, they were ambushed and the party exterminated. Lord British alone survived, but he was captured by the three Shadowlords and imprisoned in the deepest dungeon. The three Shadowlords then emerged to the surface of Britannia and started corrupting the minds of the people. The regent Lord Blackthorn himself fell under their influence, and imposed martial law and an extremist version of the eight Virtues of the Avatar.
The Companions of the Avatar (from Ultima 4) managed to avoid the influence of the Shadowlords and summoned the Avatar from his home world.
You are the Avatar, and your quest is to defeat the Shadowlords and rescue Lord British from his underworld prison.