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Harry's Muggle aunt, Mrs. Dursley, is "thin and blonde and ha[s] nearly twice the usual amount of neck" (1.2). Her first name is Petunia, which seems like a cruel joke by fate. According to ThinkBabyNames.com, "Petunia" is a "name for a humble-looking flower with white or pink blossoms." But acting humble is the last thing Mrs. Dursley could be accused of.
Petunia's flowery first name is a reminder of her connection to Harry's mother, her sister Lily. However, Mrs. Dursley's tried as hard as she possibly can to erase any connection to Lily and that magical side of the family: "they [Mr. and Mrs. Dursley] normally pretended she didn't have a sister" (1.27).
Mrs. Dursley and her husband keep Harry from learning anything about either of his parents – they don't keep pictures of them in the house, and they lie to Harry about how his parents died. Harry and his parents embarrass them. Mrs. Dursley's parents are also hardly ever mentioned; Harry is deprived of family members on a variety of levels.
When Harry finds out from Hagrid that he's a wizard, he's shocked that his aunt and uncle knew all along and didn't tell him. His aunt's response reveals a lot about her character. Check it out:
"Knew!" shrieked Aunt Petunia suddenly. "Knew! Of course we knew! How could you not be, my dratted sister being what she was? Oh, she got a letter just like that and disappeared off to that – that school – and came home every vacation with her pockets full of frog spawn, turning teacups into rats. I was the only one who saw her for what she was – a freak! But for my mother and father, oh no, it was Lily this and Lily that, they were proud of having a witch in the family!" (4.85)
Mrs. Dursley describes her sister as "dratted" and "a freak." She feels alienated by being the "only one who saw [Lily] for what she was" and by the fact that her parents didn't share this fear of and disgust about witchcraft. We're guessing that a lot of these feelings of hatred come from jealousy – Lily had powers that Mrs. Dursley could never dream of, and their parents were "proud" of Lily magical talents. There's no way Mrs. Dursley could keep up with her sister on this front, or be able to attend Hogwarts too. Instead of celebrating her sister's differences, or admitting to being jealous, she acts like her sister is some kind of monster and cuts her out of her life.