As is made clear throughout the book, mockingbirds are characterized by innocence and purity. That is why, in the words of Miss Maudie, it is considered such a sin to kill them. Dill definitely falls into the category of a mockingbird as he doesn't really mature, remaining in his original state of innocence throughout the story. There are a number of examples in the book to illustrate this point. As well as running away from home because he doesn't feel loved and appreciated by his parents Dill also likes playing childish games such as the Boo Radley game, which he invented.
Dill's status as one of life's mockingbirds is also much in evidence during the trail of Tom Robinson, who, like Boo Radley, is himself one of Maycomb's resident mockingbirds. Dill cannot understand why the prosecuting attorney Mr. Gilmer uses such derogatory language towards Tom and sneers at him during his ruthless cross-examination. Dill is so upset by such blatantly unfair treatment that he actually bursts into tears.
Unlike Scout and Jem, who are gradually becoming more and more mature due to their deepening acquaintance with the adult world, Dill remains in a state of mockingbird-like innocence, hopelessly confused and unable to make sense of a world that seems so terribly unfair.