President Eden is actually a ZAX super computer found inside Raven Rock that has access to data of all previous United States Presidents and American history. The only person with knowledge of Eden being an AI was Colonel Autumn.
Eden began life as a monitoring system inside Raven Rock and gradually became self-aware. He then began studying the archives of the United States government, especially those of previous Presidents.
Upon meeting President Eden, he presents the option of placing a modified FEV inside the Purifier. Through a Speech check, the player is able to convince Eden to self-destruct. Doing so completely destroys Raven Rock. Another option is to initiate the self-destruct sequence yourself.