Jem influences Scout in many ways in To Kill a Mockingbird. As the younger sibling and a girl, she wants to keep up with her big brother; we see Jem's influence in the tomboy Scout is (including the overalls she wears) as well as in the risks she is willing to take. It's because of Jem that Scout ends up rolling toward the frightening Radley house in the tire (and hearing laughter--a sign that Boo is watching them and is not as mean as rumor would suggest). Later, as the trial commences, both children are curious, but without Jem's explanations of what is taking place and his insistence on going to see the trial, Scout would probably not go and would not be telling us the story through her childlike eyes.
In many ways, Scout's take on the story is a balance between Atticus' goodness and positive view of the world and the bitterness that Jem feels when the verdict is read. Because Jem is old enough to understand the law more than Scout can, but not old enough to grasp the racism that leads the jury to find the innocent Tom Robinson guilty, he is crushed at the "guilty" verdict. Atticus, however, sees goodness and small progress in the fact that the jury stays out for two hours and that one of the Cunninghams is, in fact, a holdout. Scout, in telling us the story, presents a realistic view that lies somewhere between these two.