Our story, such as it is, begins in 2077. The year of the Great War; the year the bombs fell. As enormous an event as this was- it was merely the finger that began a domino cascade that had been set up months, even years prior. All of the preparations of the military, Vault Tech, criminals, moguls, scientists and even commonfolk were suddenly put to the test on October 23 of that year. We'll cover many of those as we follow the journey of 101 across the wasteland, for now let's zero in on what became known as "The Commonwealth". More specifically the C.I.T ruins which became home to the once feared Institute. When the bombs fell a number of CIT personnel took refuge in an underground level of the Commonwealth Institute of Technology. It was here that the original refugees and their progeny founded The Institute. Why is this important?
It was in the early-2250s that James, soon-to-be father of 101, escaped The Institute. James made his way to the Capitol Wasteland where he, his new wife Catherine and Dr Li founded Project Purity; a venture intending to bring clean water to the Wasteland. However, in 2258 Catherine died after giving birth to 101 (originally named Kate, after her mother) and James abandoned the project; taking his infant daughter to Megaton where he managed to gain entrance into Vault 101 for the two of them. By all accounts Kate had a relatively normal childhood, going to school, making friends and assuming Vault responsibilities as she grew older. All of that became moot when, in 2277, James left the Vault in order to return to Project Purity... an act that left Vault 101 in chaos. Now, I can't begin to guess at what James could have been thinking; that his only daughter would just sit tight inside the Vault without him? Even if she wanted to, Kate was now a target and, to many, an enemy of the Vault. She, too, had to leave.
I suppose it's possible that after nearly three decades James no longer thought about his time with The Institute. Unfortunately for both him and Kate, the Institute had not forgotten about him and were merely biding their time. James was slippery and rather resourceful and managed to (albiet mostly by accident and luck) elude their grasp on his way out. Kate was not so resourceful. As her eyes adjusted to the blinding sun outside she was ambushed by a merc named Conrad Kellogg, taken to The Institute where her personality and memories were transferred into a synthetic replica, then returned to the exact spot where she had been standing. Nothing is known about what happened to the original Kate; it's likely she was killed or imprisoned within the Institute.
It can never be said that The Institute is perfect, however. A hiccup during the transfer left "Kate" with gaps in her memories and no name. We can thank Three Dog, the local DJ, for giving her the moniker "101". More appropriate for a Synth anyway, don't you think?