Mayella Ewell represents the physical manifestation of what ignorance, racism and prejudice can do to a person. She has been abused by her father, a man that shows no regard for his family. As a result of her horrible upbringing she has little sense of self worth. Mayella envys Tom Robinson, a black man who demonstrates love for his family, kindness towards others (no matter what color) and self respect, everything she has been denied. When she reaches out to him and witnesses his "decency", something she never received from her own father, she lashes out by accusing him of attacking her. She wants to blame someone for her misfortunes.Tom Robinson possessed what Mayella yearned for, a family to love her. The idea that a black man could possess all the decent qualities she lacked deserved punishment. The fact that Tom Robinson was not responsible for her lot in life was of little matter, she was white and he was black.
I feel Mayella is also a somewhat sympathetic character. Though she is ignorant and is hurting Tom Robinson without just cause, she is a victim of her surrounding, her family, and her education (or lack thereof). Scout notices that Mayella tried to look nice for the trial, and the geraniums outside the Ewell house symbolize Mayella's desire to fit in with the town. She is a young woman in unfortunate circumstances; she can't very well go against her father's wishes--another beating or worse could come her way. Her father also probably convinced her that this would make them look good with the rest of the town, which it obviously didn't.
Atticus makes a great case when he cross-examines Mayella. More than showing that it was probably Bob Ewell who hurt her, her creates pity for her--from the townsfolk and the readers of the book.
Mayella serves as one of the antagonists of the novel. After she tries (unsuccessfully) to seduce Tom Robinson, she accuses him of rape (or is forced by her father to make the accusation).
She is symbolic of the ignorance and racism of the town of Maycomb, but is still a victim herself. Probably abused by her father, she resorts to abuse herself on someone she deems weaker (at least socially) than herself. Feeling "low class," she rages against the more socially elite of the town, exposing her insecurity, which is the foundation for her choosing to victimize Tom.
She also serves as a foil for Tom's innocence, goodness, and nobility. Tom demonstrates respect toward her, regardless of ther actions. He sees in her a victim of her father's brutatlity, thus sympathizing with her to some extent. But while Mayella can survive in this community despite her victimization, Tom cannot.