Avatar, as it relates to Ultima Online, refers to 2 distinct things.
First, it is a term for the character that the player controls within the game environment. In other words, an Avatar is the graphic that is located within the game window, as opposed to the paperdoll. While this term is not used often in UO, it is more common in other electronic games.
The Avatar is also a term deeply embedded in Ultima lore as the stranger that defeated Mondain. He is the embodiment of the Virtues and is said to return one day. Effectively, he is a "Christ Figure" in the Ultima mythology. In the single-player Ultima games upon which UO is based, he was the character under the player's control.