She is a woman who appears to be in her 20s or early 30s, and is of either mixed or Latin descent. She has apparently had "advanced knee surgery", which allows her to fall great distances without harm.
She seems to be quick-thinking, intelligent, and resourceful, as she is able to solve all of the challenges that GLaDOS throws at her.
Other than that, very little is known about her background or personality. It is a first-person game, so she is rarely seen, and her name is only known from one small mention in the credits. This should clue you in to how much you find out about her.
She is a test subject for the latest Aperture Science product, the ASHPD, and goes through all of the test chambers in exchange for cake and grief counseling. Once she successfully completes her testing, she is betrayed by GLaDOS, and only a quick use of the ASHPD allows her to escape. She makes her way through the rest of the facility, and eventually meets GLaDOS. After a short battle where Chell incinerates the different parts of GLaDOS, she is pulled outside of the facility by an unknown force, and whether she is alive or dead is unknown.
All information about her other than what can be seen and what can be assumed is supplied by GLaDOS, a self-admitted liar, so it is unknown how much of it can be trusted.
GLaDOS: You're not a good person. You know that, right?
GLaDOS: There was even going to be a party for you. A big party, that all of your friends were invited to. I invited your best friend, the companion cube. Of course, he couldn't come, because you murdered him. All your other friends couldn't come either, because you don't have any
other friends because of how unlikable you are. It says so right here in your personnel file; 'Unlikable. Liked by no one. A bitter unlikable loner whose passing shall not be mourned.' SHALL NOT BE MOURNED. That's exactly what it says. Very formal. Very official. It also says you were adopted. So that's funny too.