Ann shows little-to-no personality upon her initial appearances. George-Michael's father Michael doesn't like her for some reason and can barely remember her name or face.
Ann is later revealed to be from a conservative Christian family. Her religious beliefs soon become a major part of her character, much to the chargrin of everyone - including George-Michael.
A recurring gag is that only George-Michael finds her attractive, whilst everyone else thinks she's either plain or flat-out repulsive.
George-Michael started dating Ann as a means to distract himself from his cousin Maeby, whom he was attracted to. He weakly justifies going out with her by saying "she's really funny", despite her obvious humourlessness. Deep down, George-Michael doesn't feel anything for her, he's just trying to control his sexual urges. When Ann dumped him, George-Michael wasn't so much heartbroken as disbelieving that she would be the one to do the dumping.
G.O.B. was just as disapproving of Ann as the rest of his family. When he finds out she's dating George-Michael, he asks "is she funny or something?". After Ann turns 18 and enters a beauty pageant, G.O.B. decides that she's just attractive enough for sex. Ann then dumps George-Michael for G.O.B.
Maeby is George-Michael's step-cousin. Like the rest of his family, she despises her for no apparent reason. She was once quoted as saying that she "barely has a face". Maeby's innate jealousy over Ann once compelled her to make out with Annyoung, George-Michael's adopted uncle.