Boo is a human child who wandered into the town of Monstropolis, where the monsters work in scaring children to gather screams to power their city. There, she meets Sulley and Mike.
Since monsters, including Mike and Sulley, are scared of children and think that they're toxic, the two device of a way to return Boo to the human world without her being discovered. Later, they learn that the reason Boo was in Monstropolis was because Randall was supposed to use her in an experiment to gather more scream to solve their power crisis.
Now, aside from just thinking of a way to return Boo, Mike and Sulley should also protect Boo from Randall.
Boo's real name is Mary, as shown briefly on one of the crayon drawings she shows to Sulley in the scene where Boo is going to sleep on Sulley's bed. The actress who provided the voice of Boo is Mary Gibbs.
Mary Gibbs was so young that it proved difficult to get her to stand in the recording studio and act her lines. Instead, they simply followed her around with a microphone and cut Boo's lines together from the things she said while she played.
In early drafts, the character of Boo was written to be six years old. The writers decided to make Boo younger because it would make her more dependent on Sulley.
When Boo pulls on the stacked DVDs in Sulley's apartment and they all come falling down, the DVD she's holding can be seen to be A Bug's Life.
When Boo is in the bathroom stall she "sings" two songs. The first one is to the tune of Beauty and the Beast, another Disney movie.
When Sulley is about to say goodbye to Boo, Boo is trying to get him to play. She hands him a Jessie doll from Toy Story 2 as well as Nemo The Clownfish from Finding Nemo. The yellow ball with the red star on the floor is the ball from the Pixar animation, Luxo Jr.
After Sulley says goodbye to Boo, he closes the closet door. When Boo jumps out of bed, she has grown 7% by the time she reaches the door. The programmers had to do this as she was too short.
Boo screencaps from the movie