Why does Huck go to live with the Widow Douglas?

The Widow Douglas takes Huck in because he has no one to care for him; he is a child, and she wishes to civilize him. Huck's father cannot be trusted, as he is a mean drunk who abuses the boy, so the Widow Douglas takes on a maternal role for Huck.
Huck likes the Widow because she does not pester him about his messed-up clothes or scold him for his ways too often. She is gentle and mild—"decent," as Huck says. She represents the normal world, in which Huck feels like an outcast.
However, Huck is not content to stay with the Widow. Though he holds nothing against her, he prefers his freedom and lack of civilization. At the end of the novel, instead of returning to live with the Widow, he decides to travel west in search of more adventure.