What is the Home, and who stays there?

The Home is an orphanage. Children who have lost their parents through death and children who have been abandoned by their families stay there.
The reader doesn't know exactly how many children are at the orphanage, but I would assume that the numbers are quite high. The book takes place during the Great Depression, and many families were unable to care for their children. Lots of children wound up in orphanages. Also because of the Great Depression, not many families were financially capable of adopting children, so the orphanages got more and more crowded.
In Bud, Not Buddy, the reader meets three specific children who are from the Home. Jerry Clark is introduced in chapter one, and a family has been found for him with three little girls.
Bugs is another character who is from the orphanage. By the time that the reader meets Bugs, though, he is on his own away from the Home.
Bud, the title character, begins the story in the Home. He has been in the Home since age six, and he has been in and out of several foster homes by the time the story begins.

Six is real tough. That's how old I was when I came to live here in the Home. That's how old I was when Momma died.