So I'm just going to dive right into this, in the beginning, pre-war, you play as a happy parent and loving spouse blah blah blah, but when you enter the vault your character gets a blood test or something else like that and blacks out. You then wake up 200 years later and leave the vault thinking you passed out 200 years ago, and play through the main story until you get to a point when you realize that you are actually a clone of the person who entered the vault all those years ago, which explains your after-vault tendencies to murder people with baseball bats, or be a mountain recluse or engage in in-game fantasies of unconventional hanky-panky, whatever.
Also the settlements you can build will be able to be populated with other clones from your vault, which allows them to be voiced and have their own personalities but also allows them to be killed and make sense when they come back a week later with their same voice, looks and names.