Max has a very sharp intelligence and a strong will. If she wants something, she gets it, even if it takes bending the rules. She is somewhat pessimistic with a sense of doom hanging over her, yet she has her moments of great belief in humanity. Judgmental. Gruff on the outside, but kind and loyal to those she considers her friends. Fierce sense of justice.
Max has an extremely high esper rating. She can sense danger, and has the uncanny ability to know exactly what her opponent is about to do, as if she can, in a limited way, foresee the future.
Spoilers!
Maxine Vasser, or "Max" as everyone calls her, was born on Martian Colony 3. Her childhood was difficult. Her father, whom she idolized, was almost always away from home on business, and perhaps in over-compensation for his absence, her mother raised Max to be strong and self-sufficient. She grew up to be tough, stand-offish, and to rely on no one but herself.
Max has been a member of Banshee Squadron since its founding just before the Dominion War more than ten years ago, though during the lull after that war she took a brief hiatus to fight on the Federation borders as a mercenary. In 2380, the Banshees were re-formed, and Max fought in the Kelvan Incursion, the First Mulluran War and the Second Mulluran War, almost single-handedly destroying an entire enemy supply convoy during that conflict.
In 2374, her best friend and wing commander, Jazz Phoenix, was encircled and presumed killed by Jem'Hadar attack craft while on a misison in the Cardassian Badlands. Max blamed herself for not being able to save Jazz. In 2383, Jazz was found alive on a Cardassian prison planet and rescued by the Banshees, but shortly thereafter was killed in the dilithium mines of Rostella IV while defending the lives of her teammates. Max blamed herself for Jazz's second death as well.
She became entangled in one of West's adventures when he ran into her while searching for her dead father while she was visiting the grave. Her father turned out not to be dead after all but merely hiding from the evil Section 31, but he was killed while defending his daughter and West from Section 31. Max blamed herself.
Her encounter with Section 31 left a sour taste in her mouth. She began questioning her loyalty to Starfleet and the Federation for letting an organization like Section 31 exist within its operating mandate. She resigned her Starfleet commission and teamed up with West on his quest to poke a thumb into the eye of evil and make a little side cash.