In the beginning, God created Todd Howard, and gave him a very annoying voice. And then Todd Howard made Fallout 3, which was the best creation that mankind ever got, and God was jealous, and so he made there we a plot point where your father dies. Um... Okay, maybe that's not what happened, actually, that's definitely not what happened... Let me back up a bit.
The ACTUAL Story of Fallout 3
On October 23rd, 2077, a nuclear war happens that devastates the Earth after many years of wars. This turns most of the world into a big wasteland in two hours. Then Fallout 1, 2, Tactics, and Brotherhood of Steel happen, two of which sucked and you shouldn't play. Anyways, you were born in Vault 101, a vault in the Capital Wasteland around what used to be Washington D.C.. Anyways, you've been told you were born, raised, and molested in the vault, and your daddy is just a boring doctor. After growing up and stuff, one day your dad leaves the vault (which was, from what you heard, impossible) and causes mass hysteria around the vault. Your lady friend Amata suggests you leave, so you do, and then you go to the nearby town of Megaton. In Megaton, you meet Colin Moriarty, who tells you that your daddy passed by here years and years ago, and tells you you weren't born in a vault. He also tells you (for a fee) that your daddy went to Washington D.C. to meet the almighty Three Dog, who is a disk jockey for the radio station Galaxy News Radio. He tells you (again for a fee) that your dad went to Rivet City, a city the is actually a boat. He also tells you that you weren't born in a vault, but you just ignore him and go to Rivet City. There, you meet Dr. Madison, who had worked with your father many years ago on something called Project Purity. She also tells you you weren't born in a vault, and sends you on your way to Jefferson Memorial, where your father went (this time for no fee). There, you find a bunch of tapes which say that your father went to Vault 112. You go there, and enter this virtual reality thing. In there, you meet virtual people, and this virtual girl named Betty, who asks you to do increasingly evil things, at first things like making a boy cry, then to making a married couple divorce, then to killing all the residents. Of course, there's a non-evil way of doing this, which involves activating a computer and running a fail-safe, or something. Anyways, it turns out your dad was the dog, and you exit the virtual reality. You meet up with your dad, who explains that you weren't in fact born in the vault (no, really?) and that Project Purity is an attempt to build a giant water purifier in the remains of Jefferson Memorial. You both go to Rivet City, and convince Madison to help you with project purity. You, dad, Madison, and a few other scientists go to Jefferson Memorial to continue work on the project. After doing a couple fetch quests, the Enclave, who are the remnants of the government, and are evil, show up and kill your dad. You and the scientists escape to The Citadel, which is a place that's occupied by the Brotherhood of Steel, who are the good guys, basically. Madison explains that you need a G.E.C.K., which is a device that was designed to let you create life out of nothing after the war. Then you go to Little Lamplight to get into Vault 87. Once you get the G.E.C.K., you are captured by the Enclave, and have to escape (using the art of murder). You meet President John Henry Eden, who offers you the chance to infect Project Purity with the F.E.V. (Forced Evolutionary Virus). Anyways, you go back to the Citadel with the G.E.C.K., and then you become a part of the freaking Brotherhood. Awesome. So then you and the Brotherhood take back Jefferson Memorial, with the help of Liberty Prime, a giant death robot. Once you take it back, the place is going to blow up. Great. But whoever tries to save everyone else will die from radiation. You can go in, you can infect Project Purity with the F.E.V. (which actually kills anyone not born in a vault), or you can just sit there and die (it's more complex than that, but... Just do yourself a favor and play the game).