Project Purity is a water purification project held within the Jefferson Memorial in Fallout 3. It was originally started by a group of scientists including Dr. Li and James over 20 years before the setting of Fallout 3. They originally had the support of the Brotherhood of Steel but they eventually had to pull out to focus on more important issues in the Capital Wasteland. No long after, James' wife died while giving birth to you, this lead to him abandoning the project and entering Vault 101 for your protection. James' departure was the final straw for the Project Purity team, they had nobody to protect them and their lead scientist had disappeared. Project Purity was abandoned and the rest of the team went their separate ways.
Around 20 years later, James left Vault 101 to restart work on Project Purity. While in Vault 101 he had discovered that he needed a G.E.C.K in order for the project to work. With the help of his son, he managed to recruit some of the old team (including Dr. Li), clear the Jefferson Memorial of Super Mutants and restart Project Purity.
Shortly after restarting the project, the Enclave attack the Jefferson Memorial and capture Project Purity but it's useless to them without the G.E.C.K. James sacrifices his own life to help you escape from the Memorial. After James' death, you manage to retrieve the G.E.C.K from Vault 87 and the Brotherhood agree to help remove the Enclave from the Memorial.
After fighting you way the control room of Project Purity you're given four options. You can sacrifice yourself to activate Project Purity, you can make Sarah Lyons activate Project Purity which will kill her, you can infect the purifier with a modified FEV virus given to you by President Eden or you can just do nothing and wait for the Purifier to self destruct killing everyone in the room.