A dynamic character is one who changes over the course of a story (as opposed to a static character, who never changes). Tom Sawyer is certainly a dynamic character. The Adventures of Tom Sawyer is in part a coming-of-age story in which the titular hero makes his first steps into the adult world.
Tom begins the novel as a mischievous young boy more interested in having fun and shirking responsibility than anything else. He sometimes even fancies himself a rebellious nonconformist, proudly spending time with social outsiders like Huckleberry Finn, much to the shock and rage of his disapproving elders. However, Tom begins to change as the result of his adventures.
Responsibility becomes a major motivator in his behavior. He accepts the blame for a schoolbook that his love interest Becky rips, taking the punishment chivalrously in her stead. He testifies against Injun Joe to save the framed Muff Potter, even though this puts his safety at risk. By the end of the book, Tom is even recommending the respectable life for Huck Finn, the one person whose fun-and-fancy-free lifestyle he used to envy and admire. These changes are significant proof of how Tom's experiences have changed his outlook on life.