Ava was raised in Vault 101, a closed underground facility located just outside Washington D.C. Her father, James, was the Vault's chief medical officer, at the constant beck and call of the Vault's residents, and it was expected that Ava would one day follow in his footsteps; the young Ava had a clear aptitude for science, although her bedside manner left something to be desired. Even as a child Ava never really felt like she fit into Vault life. Forever at odds with its artificial sense of community, she had few friends amongst her peers, and developed a reputation for being needlessly "difficult". She stopped trying to ingratiate herself during her teens, preferring to spend most of her time with her father or his assistant, Jonas. That all changed on the morning of Ava's eighteenth birthday, when she awoke to find Jonas dead, her father missing, and the Vault in a state of chaos. Despite the Overseer's attempts to try and detain her, Ava managed to recover a weapon and escape into the Capital wasteland.
Her search for her father eventually brought Ava to the east coast chapter of the Brotherhood of Steel, who had supported James and other scientists on an elusive mission known as "Project Purity". It was from the Brotherhood that Ava discovered the truth: far from being born in Vault 101, Ava and her father had actually sought sanctuary in the Vault after Ava's mother died. In doing so, James abandoned the Brotherhood and Project Purity, resulting in the project being shuttered indefinitely. Now that Ava was of an age, he had returned to the wasteland in order to see the Project completed. James subsequently sacrificed himself in order to stop Project Purity falling into Enclave hands at the Jefferson Memorial, leaving his daughter to finish what he had started.
Working with her new allies in the Brotherhood, Ava went on to recover the G.E.C.K. from Vault 87 and, with the help of Sentinel Sarah Lyons and the super mutant Fawkes, activated Project Purity, successfully delivering clean water to the people of the Capital wasteland. In doing so, she gave the Brotherhood their first major coup in the region, thereby strengthening their claim.
Ava was formally inducted into the Brotherhood's ranks under the enthusiastic sponsorship of Sentinel Lyons, and the two became close advisers and personal guard of the young Arthur Maxson. Following Sarah Lyons' premature death, Ava worked to support the newly-minted Elder as he assumed leadership of the East Coast chapter. She was one of the few people Maxson trusted to lay the groundwork for the Brotherhood's expansion, and would later lead a squad performing reconnaissance and field preparation ahead of the Prydwen's arrival. Having seen the thankless way her father was treated by the residents of Vault 101, the Brotherhood managed to prove that it valued Ava and her skills, giving her a sense of purpose and tangible recognition of her achievements.
In 2286, Ava and her squad were dispatched to the Commonwealth wasteland in order to investigate rumors of Institute involvement. Upon arrival, however, they found themselves separated by Courser synths, with the Institute dedicating its most efficient agents to trying to neutralize the Brotherhood's prized assets. By the time the Brotherhood officially deployed en-masse in Massachusetts, only part of Ava's squad had been successfully recovered. With Maxson's ground war picking up momentum, and no news of her missing team, Ava finds her skills as a Sentinel more in-demand than ever before.
Ava in the New England Commonwealth, circa 2287. Unlike previous Sentinels, Ava prefers to wear light armor rather than the full suit of Power Armor - she claims it's better for her maneuverability.
A note on Ships
I'm going to break with tradition here and say that Ava/Maxson is most emphatically not a thing: Maxson probably has some confusing, not-entirely-platonic feelings for Ava, as he did for Sarah Lyons, but she has difficulty seeing him as anything other than a little brother despite the fact that he's her direct superior. Their relationship is complicated enough without the inclusion of romance, imo. Ava/Butch was briefly a thing back when they were both eighteen and new to the wasteland, but they decided they were better as enemies-turned-friends without adding "-turned-lovers" to the end of it. Ava hasn't committed to anything since joining the Brotherhood; she is, as they say, "married to her work", for better or worse..