In "The Adventures of Huckleberry Finn" what does Twain accommplish by using Huck as narrator?

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!