Dill ran away from home because his mother got married and he felt that the couple did not need him.
The Finch children got used to Dill coming for the summer, but one summer he did not come. He sent a letter saying that his mother got married, and his new father was going to build a fishing boat with him.
His father was a lawyer like Atticus, only much younger. Dill's new father had a pleasant face, which made me glad Dill had captured him, but I was crushed. (Ch. 12)
Unfortunately, Dill’s new father turns out to ignore him as much as his mother does. His parents sit and read, and don’t need him. So he takes the train to Maycomb and Scout finds him hiding under her bed.
With Dill, it is often hard to tell what is a whopper and what is true, but this incident demonstrates that Dill considers the Finches more of family than his own. He goes to them and his aunt Rachel when he feels abandoned by his mother, and Atticus of course allows him to stay because he realizes how important family is to someone like Dill who does not have one.