This scene is meant to reveal more about Atticus to Scout. When he kills the mad dog--and does so expertly, with one shot--it shows Scout that there is more to him than a lawyer and a father. He knows how to shoot and he's good at it.
> “Take him, Mr. Finch.” Mr. Tate handed the rifle to Atticus; Jem and I nearly fainted.
This illustrates my point well; Jem and Scout have no idea about him, really. This also develops Atticus's character for the reader. He can shoot and he's good at it, but he hates to and he hasn't in thirty years. It can also be seen as a symbol for the entire Tom Robinson trial.