
heres the plot explanation on wikipedia:
The game is set in a post-apocalyptic world following The Great War, a nuclear war that occurred on October 23, 2077 and lasted less than two hours but caused immense damage and destruction. Before The Great War were the Resource Wars, during which the United Nations disbanded, a plague rendered the United States paranoid, and Canada was annexed.
The game takes place in 2161 in Southern California and begins in Vault 13, the protagonist's home. Vault 13's Water Chip, a computer chip responsible for the water recycling and pumping machinery, has broken. The Vault Overseer tasks the protagonist with finding a replacement. He or she is given a portable device called the "PIPBoy 2000" which keeps track of mapmaking, quest objectives, and various bookkeeping aspects. Armed with the PIPBoy 2000 and meager equipment, the protagonist is sent out into the remains of California to find another Water Chip.