In the Toy Story movies, Andy's mom is a pretty unimportant character—she's mostly just there sometimes adding a little realism to a story about toys that talk, walk, and have feelings. However, Joe Negroni, the author of The Pixar Theory, has a fairly interesting idea about Andy's mother that makes her way more interesting and integral to the central plot of the movies.
The gist of Negroni's theory: Andy's mom was the little girl who owned the Jessie cowgirl doll that she left in a box on the side of the road so many years ago. Inadvertently, her son Andy ends up with Jessie in present time, and, though not consciously, Jessie was reunited with the girl who casually ditched her. You can read his full take on the theory here.
If you feel like re-watching any of Toy Story movies thanks to this post, have fun sobbing violently, because those movies just manage to have that effect on grown-ass adults. No shame.