Background
She was born to an average family in a well-to-do community on Bothawui, where she lived a happy and carefree childhood until she was four. At that point, a terrible disaster struck their home planet, and Vexa was the sole survivor of her family. Dealing with their own grief, many in the community passed Vexa around without much love or care (out of duty, mostly) until she was old enough to technically be able to fend for herself. She basically became a "street rat," and stole to survive.
When she was a little older, she stowed away on a ship and made it to another planet called Randon. While living there, she stole from the wrong person and was taken by a gang. But instead of killing, beating, or punishing her, they took her in and made her one of their own. This was done by Romias Prost, a fellow Bothan. They took her under their wing and made her a part of their thief organization.
That organization's name was Valence, and only rumored to exist. They, led by Andros Moy, hit high profile targets, working in small groups within the larger whole of Valence. Vexa stayed close to Romias, but bonded with a Twi'lek named Keda Byrillo. Their crew was rounded out by Ais Dalu and Bardo Kishi.
Vexa spent most of her waking moments with one or more of her crew, and their bond and ability to work together allowed them to move up quickly through Valence. When she wasn't doing jobs for them, she works quietly to acquire and sell small trinkets and knicknacks on the side. She sold them through her black market contact Vyn Corso.
Eventually, Vexa got a message from Valence about a specific new job, one where everything seemed more secretive than normal. Andros himself gave the information, saying he would be joining the crew for the job. Whoever gave the job didn't give the normal amount of information, instead just bare basics to arrive somewhere, and that someone else would give them more information at that point. It wasn't wholly unusual, but odd enough with all the other factors to make the crew wary.
Vexa's mission took her to the Kwenn Space Station. They made it through the shuttle bay without issues, almost too easily. They proceeded down the hall they were told to go, noticing a large Imperial presence at the station. Though Valence usually hit high profile targets, they had never done a mission against the Empire. At least, not that Vexa had ever heard about.
Down the hall, the group was immediately ambushed by Storm Troopers. Vexa, who brought up the rear, was far enough away to catch the silent warning rippled through Romias's fur and escape. She made it back to the bay, where she escaped through a maintenance pod to the planet Kwenn. Before leaving the Space Station, she saw the Empire shoot Andros through the head.
On Kwenn, she worked out a plan to go back and try to rescue her crew. She managed to confirm that at least Keda was still on the Space Station, and couldn't find any information on where they had taken her other captured crew members. However, she didn't make it into the landing bay before she was caught.
Because she committed three major crimes: espionage, escaping, and breaking back in, they threatened immediate death instead of jailing or otherwise capturing her. She managed to convince them to let her board the slave transports heading to the Hutt planets instead.
She lived as a slave to Pido the Hutt for months, with him always reminding her that she would likely be dead if he had not decided to buy her. She lived outside the palace where she was mostly left to her own devices, unless Pido had a job he wanted her to do.
Eventually, he promised her freedom if she would undertake a dangerous mission to Eriadu to deliver a ship Pido lost in a bet.
Along the way, she was able to find and rescue the two remaining members of her crew still alive: Ais and Keda. Ais, held in an Imperial reeducation center, and Keda, sold to Lobug the Hutt, had been through enough. A contact was able to get them to safety, a hidden planet that Vexa could only know about if she decided to go and never leave again.
But her adventure had taught her something: that there was more to life than just stealing to survive. Something proactive had to be done.
Over the next decade, Vexa joined the Rebellion and became an integral part of the Bothan Spy Net. She never visted Ais or Keda, despite her former romantic feelings for the former, and her deep love for both. She relayed messages from time to time through the contact. Ais and Keda got married and settled down, the proud parents of two hybrid Twi'lek/human children.
Vexa found meaning in her work. She worked on her skills and was able to become a master at her craft.
When her new crew within the Spy Net were sent to investigate a suspicious trade route, they were again captured. But this time, Vexa was more prepared and more capable. She hides on the ship, avoiding detection as she works out a way to free her crew members.
Motivation
Deep down, Vexa believes in the criminal way of life. She thinks it's the only way to play the game, as it seems to be rigged against all but the most fortunate. She believes in making her own fortune, whether honorably or not. She has had a questionable moral compass in the past (especially when it comes to smaller infractions), but is fiercely loyal and believes in the freedom of the Rebellion.
Vexa supports the idea of black markets, mercenaries, and other groups that fall outside of the law.