Andy's mom has always been a bit of an enigma. In the first Toy Story, we barely even saw her face. That's all fine because throughout the movies, the real focus has been on Andy and the love he has for those toys.
But this is Pixar, and it stands to reason that there is more than meets the eye when it comes to the Davis family (Andy's last name).
In order to understand who Ms. Davis really is, we have to start with something seemingly simple: a hat.
In the picture below, you see Andy's cowboy hat that he plays with throughout his childhood. Study it closely.
Notice anything weird about the hat? It looks nothing like the hat worn by his favorite toy, Woody. Why wouldn't Andy wear a hat that was brown?
We don't think about it because most of us are normal human beings with things like jobs and tax exemptions. But I want you to take a quick journey with me: Andy got this hat from his mom.
In Toy Story 2, young Andy Davis left for summer camp, and his mom held a yard sale. "The Chicken Man" found Woody in one of the boxes (he was trying to save a fellow toy) and pleaded with Ms. Davis to sell him because Woody is a collectible from the 1950s.
Ms. Davis refuses, acknowledging that Woody is "an old family toy." Not that much time has passed between the Toy Story movies, but we know that Andy has had Woody since Kindergarten, according to Mr. Potato Head. Andy's 6th birthday is in the first Toy Story, which makes him 7 or 8 in this movie. Woody doesn't seem all that old in comparison.
Further, Woody has no recollection of who he is. Many have suggested that this is because he was owned by Andy's father, who is never mentioned in the movies. Molly is a baby in the first movie, which means Andy's father either died or walked out not long before the movies started.
A reasonable assumption is that Andy's mom gave Woody, his father's toy, to him on his 5th birthday. After all, she gave him Buzz Lightyear on his next birthday. If Woody had been a new toy when Ms. Davis gave him to Andy, then he would know exactly who he is was, which is unlikely because he is so rare.
Now, back to the hat. I believe Andy received the hat from his mom, as well. There's another instance in the movies when this hat is shown:
Notice anything familiar? That is the same red hat with a white lace. Why would Andy have a hat that looks exactly like Jessie's? Because his mom did. Look at this:
See that hat on the bed? Emily, Jessie's previous owner, wears that hat throughout the "When She Loved Me" sequence in Toy Story 2. The sequence clearly takes place in the 60s and 70s, as evidenced by the decoration and qualities of Emily's things.
That is about as 1970s as it gets.
That makes Emily the same age as Andy's mom, who had him in the 80s. They also have the same hat, except the white lace on Andy's hat is missing, but you can clearly see where it once was. There's even a faded mark:
That makes this an old hat.
We know that Emily donated Jessie and her other "cowboy" accessories as a teen, so wouldn't the hat be included? If you watch closely, the hat isn't in the box. The box isn't even big enough to hold it.
We do see that Emily has short, auburn hair. It almost looks like...
Albeit her hair in the movies is lighter. Age is funny like that. And yes, Andy's mom is Emily, Jessie's previous owner.
Now you may be wondering if Emily/Andy's mom noticed that Andy suddenly had a toy she once had as a child. Think of it this way: how would you react if you saw that your kid had a toy that looked like one that you had? You probably wouldn't assume they're the same, even if you're in a Pixar movie.
The theory is that in a twist of fate, Emily (Andy's mom) loved a cowboy toy but gave it away during her adolescence. Her son would grow to love a cowboy toy as well, in a weird way that resembles the strong love she once had. She passed the hat down to him, and as destiny would have it, Andy would one day receive Jessie, as well. This would redeem his mother's abandoning of her, making Emily's story come full-circle.
And much like Emily, Andy also grew tired of his toys and moved on. He also gave them away and let them go.