Several things. First of all, he creates a highly entertaining story. Huck is a very funny character with a lot of unique perspectives and conclusions. His attitudes about being civilized, about prayer, and about many different things are pretty funny. Also, he is young enough to be in that time of life when he and his friends are planning pretty funny things to do; consider chapter 2, where Tom Sawyer and he form a "gang" that plan on robbing, kidnapping, and plundering. Their descriptions and plans are all funny, considering they don't even know what ransom is and some of the boys break down and start crying because they miss their moms. His age creates for some very funny situations, along with his unique perspective.
Most importantly, Huck provides a way for Twain to satirize. Twain makes fun of almost everything, and he uses Huck to do it, safely. Huck can go around forming opinions about everything-opinions that, if given by a learned adult like Twain, might be considered offensive. He makes fun of religious people, the deep south, scamsters, old ladies, rednecks, slave lore, interior decorating, feuds, circuses, the bible, and just about everything else under the sun. And, he uses Huck-a naive, innocent and unique-minded kid-to make those opinions believable. Huck is the perfect vessel for Twain to safely make fun of things he feel really should be made fun of.
Another reason that Huck works well is because he is a good character to use to present the crisis of morality that comes with trying to decide if slavery is right or not. Huck wasn't raised in a "traditional" home; he didn't have parents to tell him what was right or wrong. So, he learned to have an internal compass, to decide for himself whether something was right or wrong. He had to live on his own. Because of this, he helped Jim whereas some other southern boy might not have for fear of getting in trouble. Huck had that same fear himself, but helped anyway. Huck's unique background gives him the crisis of conscience that he struggles with the entire novel; he feels bad for helping a slave, but decides to do it anyway. Some other kid might not have had the proper background to be able to do that.
I hope those answers help; good luck!
Mark Twain was the first American writer to use a child narrator for a novel, a technique that would be employed by later authors such as Harper Lee in To Kill a Mockingbird. Huck is able to describe society and its hypocrisy in ways that only an uneducated, innocent child could do. Twain could not have written such a scathing critique of American society as a work of nonfiction with himself as the narrator, but Huck gives Twain the freedom to state the obvious that "polite Southern society" refrained from speaking.
Twain also achieves a considerable measure of humor by using a child to narrate the story. Huck's observations on heaven and hell, organized religion, the King and the Duke, for example, are amusing, while his descriptions of the decor in the Grangerford household are downright hilarious. His unawareness only serves to increase the humor.
My answer can be summarized in a few words: which would you rather read: a story told by an adult who is completely removed from the story, or one by a child who is experiencing these events as they happen? I, personally, would love the latter, but that's just me. The previous two answers are wonderful. I probably just over-simplify things.