The Lone Wanderer is the only playable character in Fallout 3. The character can be male or female depending on the players choosing. This person was born in the Jefferson Memorial and was delivered by Dr. Li, this person's parents were James and Catherine. Shortly after giving birth Catherine died at the scene which led James to abandon his work on Project Purity and enter Vault 101 for the protection of his child.
The Lone Wanderer spent 19 years within the Vault, then one day James left without any explanation. The Vault 101 Overseer was furious that James had broken the rules and he believed the Lone Wanderer knew something about it and put out a warrant for his arrest. With the help of the Overseer's daughter Amata, the Lone Wanderer manages to escape from Vault 101 and heads out into the Capital Wasteland in search of James.
There is also speculation that the Lone Wanderer may in fact be a decendant of the original Fallout protagonist.