Huck speaks in the uneducated dialect of his hometown of St. Petersburg, Missouri, reflecting the fact that his schooling has been erratic under the guardianship of his alcoholic father. The opening sentence of the novel gives us the flavor of Huck's speech:
You don't know about me without you have read a book by the name of The Adventures of Tom Sawyer; but that ain't no matter.
Huck writes as he speaks, not according to standard grammar and using words such as ain't. This makes the book a challenge for nonnative speakers, but it also makes Huck a colorful, believable character with a voice all his own.
Beyond that, it shows that Huck lives in a gray area on the fringes of respectable white society. Huck's status ambiguity is made clear in Tom Sawyer, in which Tom is both filled with admiration of Huck for his freedom, such as not having to attend Sunday school, and a sense that this alluring boy is an outcast with whom he should only associate at night or when other boys aren't around.
Huck's status ambiguity continues as this new novel opens. The town wants to "save" and redeem Huck from his circumstances and fully integrate him into what Huck calls "sivilized" society, which is how he ends up living at the Widow Douglas's as the novel opens. But Huck also rebels against this restricted lifestyle.
Huck's language reflects the way his outsider status makes it possible for him to perceive reality more clearly and with more commonsense than is possible for someone more fully indoctrinated in the values of his racist society (though Huck also struggles with the anguish that these values, to the extent he internalizes them, causes him).