The unnamed carnival woman was the biological mother of Herbert Powell.
When Abe Simpson visited the local carnival at Shelbyville (before marrying Mona Olsen), he was drawn to the young female worker at first sight. She had sex with him for his money. A year later, when the carnival returned to Shelbyville, Abe discovered that she had given birth to their son.
Unmarried and ashamed, Abe and the woman took their infant son to the Shelbyville Orphanage. What happened to her after this is a mystery. Their son was later adopted by the Powell family and renamed Herbert Powell, who went on to be the founder of Powell Motors in Detroit, Michigan.
Young, beautiful and attractive, it's no wonder that Abe fell for her at first sight. Her son Herb seems to have interited very little from her, because he bares a strong resemblance to his half-brother, Homer Simpson.