Annette is the wife and colleague of William Birkin and mother of Sherry Birkin. She was a research assistant to William before the two married. Prior to the outbreak caused by James Marcus, William and Annette were very loving parents to Sherry but after William almost died escaping the underground facility he became extremely paranoid and saw the G as his life's work.
Resident Evil 2
Annette who had helped her husband design the G-Virus, extracted from Lisa Trevor, was pulled into Williams obsession in completing G and thus the two started to ignore Sherry. Williams paranoia transferred to Annette as she became suspicious of a woman snooping around Raccoon City trying to find out more about Umbrella and the G-Virus. She learns that the woman, Ada Wong, is in fact a spy for a rival pharmaceutical company and is trying to obtain a sample of the new virus.
Towards the end of G's development William decided to sell G to the US Government instead of taking the reward that Umbrella was offering (a seat on the executive board). Annette was present in the underground complex when the Umbrella Special Ops Team lead by Hunk fired on William who refused to turn over the Virus. William injected himself with the G-Virus in an attempt to save his life, however it transformed him into a mindless monster bent on destroying all he came across and procreating. A G-Virus subject is most compatible with someone of the same gene type (sibling, parent, offspring) and is drawn to them.
Annette spots Ada skulking around in the sewers and armed with the knowledge of who she really is, why's she's there and a firearm, Annette opens fire on the female agent. Leon stumbles upon the scene and rescues Ada who is pinned down and unarmed. Annette flees and Ada purses her.
Some time later Leon and Claire encounter Annette in the underground research facility. Annette learns that Sherry is no longer in the Police Station, but in the sewers she warns Leon & Claire that William will be after her. Annette then makes her way to the underground labs. Annette has one last encounter with her husband, now in the third stage of his mutation. She can see the remains of his face on the chest of the beast in front of her and shoots at William as he charges her with his clawed hand. Leon and Claire discover her body and can only watch as blood flows out of her body. With her final breaths, she gives Claire and Leon the location of the antidote needed to cure Sherry and a message for her daughter saying that even though she failed her as a mother, Annette always loved her.
(Note the above is the scenario presented in Resident Evil: The Darkside Chronicles. In Resident Evil 2, the above could happen or Annette dies after suffering injuries due to the facility coming down around her)
In the non-cannon Leon A/Claire B Scenario follows much of the above except she corners Leon in a corridor and informs him of Ada's true purpose in Raccoon City. Leon doesn't believe her but Annette is about to shoot him when the ceiling falls on her. Leon leaves her and as he is on the walkway back to the breaker Ada arrives and draws her gun on him. She threatens Leon who refuses to surrender the G-Virus. Ada can not bring herself to shoot Leon but is in turn shot by Annette who dies from internal trauma suffered from the previous encounter.
In the Claire B part of the story, Claire encounters her in the sewers and even saves her from the mutant alligator (if Leon didn't kill it the first time around). After Sherry is cured of the G-Embryo she talks to her mother who apologizes for neglecting her but lets her know she truly loved her. Annette dies in her daughter's arms.
Annette appears to be an expert marksman as she managed to disarm Ada Wong (shot the weapon from her hand in RE2 and out of her reach in Darkside Chronicles). In Resident Evil 2 she uses a Browning Hi-Power 9mm pistol. In Darkside Chronicles it has been upgraded to a Glock 17.