First of all, Huck was one of the main characters in his previous novel, "The Adventures of Tom Sawyer". So, it was convenient to carry on part of that storyline through Huck Finn in the next book.
Secondly, Huck is a young kid with a very unique mindset that works well for Twain's desire to satirize many elements. Kids often state things how they really are, or comment on things in a very unique and funny way. Huck, with little formal education, few lessons in civility, morality, or manners, is the perfect voice for many of the judgments that Twain passes on people in society. We see Huck as he struggles with the concept of formal religion, his conscience in regards to slavery, his opinion on the Duke and the King, and along the way, every sort of person that you could possibly imagine. As a kid, Huck tends to approach these people and situations with an open mind, which allows Twain to describe what is going on without bias. Eventually, Huck makes comments or judgments, which allows Twain's bits of opinions to come through in a non-offensive way, because he's just Huck, a funny kid on the run.
It's Huck's story. It's told in his language and his words with his feelings, thoughts, and reactions--regardless of how well he understands the situation. No one else could tell the story as he could and have it be believeable. We would never get to know Huck the way we do and watch him grow from a child into a young man with principles and values if it weren't told from his perspective. Granted, Huck is unrealiable in many situations since he has not the knowledge and understanding of the events (for instance, the town mob scene, the con job of the King and Duke, the irony of the Shepardsons and the Grangerfords killing one another and acting as "gentlemen" otherwise), but he is the one who is present for the entire ride down the river with Jim. He is the only suitable choice for the narrator...it wouldn't be the same story with the same outcome if he switched point of view among characters or if he had some third-person omniscient narrator reporting Huck's experiences.