Carol is a sweet, doting, and soft-spoken woman, though often meek and previously defenseless when it came to facing her husband Ed. Throughout her stay at the survivors' campsite, she remained extremely protective over her daughter, shielding her from the dangers of the outside world. After Ed is beaten half to death and later killed, she gradually begins to develop thicker skin and draws a newfound boldness inside of her.
As opposed to her comic book counter-part, Carol in the TV series is stronger and more independent as the first season moves along. The inclusion of Ed as her husband, according to Robert Kirkman in 'The Walking Dead Chronicles', was to give her a solid foil to produce the strength needed to survive where the comic book version wouldn't have.
Carol lived in the South where she eventually met a man named Ed. He was charming enough at first that she felt comfortable dating and marrying him, however his true nature would be revealed the longer they stayed together. She was a housewife, and fiercely looked after their daughter Sophia, nurturing and providing her with comfort while Ed greatly neglected her (much to Carol's disgust).
Throughout their marriage, she was a victim of verbal and physical domestic abuse. Because of her independence being shattered, she remained hesitant to tell any outsiders about her situation.
During the outbreak, she, Sophia, and Ed traveled toward Atlanta which was supposedly a safe-zone. While on the road, they meet Shane, Lori, and Carl. With the city being destroyed by the military, all of them meet up with other survivors and form a campsite on the outskirts of Atlanta.
Carol Peletier was Sophia's mother and one of the survivors of the original Atlanta band.
Not much is known about her pre-marital days. She had always had a good relationship with her sister, and specifically when she was a teenager, had dated a share of guys. She had dated her husband for a significant amount of time, before he eventually talked her into marrying him (the proposal she only accepted because of her fear of being without someone). It's been heavily implied that she faced little satisfaction throughout her many years of marriage and only stayed with him because she both needed as much help as she could get taking care of Sophia and also because of the needy tendencies.
Her husband was the breadwinner of the family, working as a successful car salesman. Because of the large amount of money he brought in daily, she herself didn't have to venture out into the working world, so she played the role of an average housewife, although she occasionally brought in some extra money by maintaining an at-home business where she would sell tupperware out of catalogues (though her customers mostly tended to be just friends and family). She tended to indulge in a lot of arts and crafts during her free time, whether it be knitting or scrap booking (the latter she had frequently been taking classes for).
Once the apocalypse broke out, her husband had the misfortune of being forced to watch his parents die in front of him, and supposedly become zombies. After this event, he was driven into a deep depression, and Carol's relationship with the man had become increasingly strained. Even despite talking a distressed and doubtful Carol into staying with him, he ended up giving up on life eventually and committing suicide, leaving her and Sophia all alone. Shortly after his death, Carol had decided the best next move for the two of them would be to move to Atlanta to be with her sister, where they both would be safe and secure from the zombies.