Veronica is Chef's former girlfriend/fiance, who was revealed to be a Succubus in the episode The Succubus.
Apperance
Veronica has two specific form. Her human form is that of a moderately attractive brown haired woman, who is slightly taller than Chef. She is often seen wearing a a green dress held at the waist with a blue belt, and blue shoes. She is later depicted in a frilly wedding dress.
Veronica's true demonic form
Veronica's true demon form however is that of a demented, massive beast of a woman, with low-hanging breasts, cloven hooved legs, blood red eyes, potruding fangs, and large leathery wings. She does not appear to wear any clothing in this form save for a loincloth.
History
Chef first met Veronica while searching for Karma Suitra books at the library. Using her hypnotic song ("There's got to be a morning after"), she tricked Chef into spending the night talking to her about "the goddess" and the evils of men, and forcing him to fall in love with her. The boys however grew suspicious of Veronica's behavior, primarily out of jealousy of loosing Chef to hear. However after talking to Mr. Garrison, the boys realized that she was in truth a demonic Succubus, a demon sent from Hell to suck the life out of men and that it's best to just "screws them and leaves them". The boys soon discovered that Garrison was right (However Garrison wasn't speaking in the litteral sense when he told the boys this), when she revealed her demonic form while visiting Cartman's house. The boys attempted to warn Chef, who did not believe them and cast them out.
After doing research, the boys soon discovered that in order to defeat Veronica, they would need to force her to listen to her own song backwards. They did so at the wedding, causing her to reveal her true for to not only Chef, but to his parents and the rest South Park. After she managed to kill Kenny, Stan and Kyle sang enough of the song to thus cast Veronica to the pits of Hell from wence she came.