Laura (Avery) is Arthur Avery's ex-wife. Edit
Laura is the mother of Cather Avery and Wren Avery, the twins, and the ex-wife of Arthur Avery.
When the twins were in 3rd grade (about 9 years old), September 11th happened. That was also the day Laura left the family.
The two young, naive girls were sent home early from school that day. They saw their parents arguing and simply assumed that they were upset and worried about the crazy events of that day. What they didn't realize was that their mother was unhappy and that she would literally walk out of their lives that night.
Arthur- Divorced several years before Fangirl takes place. While Wren and Cath are in college for their Freshman year, Laura contacts Arthur and they simply chat. Laura claims she'd like to help out with the girls, and Arthur is too naive to understand that the girls (at least Cath) will be furious.
Cather- Cath came to reality far quicker about the situation than Wren did. Their mother left. She completely walked out of their lives. When Laura tries to come back while the twins are in college, Cath completely ignores her. She believes that Laura walked out when the family most needed help, then wants to come in once everyone's standing strong and say that she helped the family's development.
Wren- Wren missed her mom when she walked out. When Laura talks to her in college, Wren is extremely happy to have a mother back. They hang out and Wren even accepts a Christmas present from her. Any anger she had towards her mother in the past fades.