He is also introduced as liking sports at an earl age. This tells us that he is very outgoing. This is important because throughout the story Jem and Scout get into trouble involving being physically fit. For example, when German jumped the fence to get away from the brother of Boo Radley, it's a good thing he was physically fit otherwise he could have ripped a little more than just his pants.
Also, being physically fit, I think, made Scout want to look up to Jem even more. Seeing as Scout enjoys physical activities herself, having an older relative in her immediate family gives her more to do. In that way, the story involves the two children in their adventures, not just Scout.
Jem, I think, is portrayed perfectly to be a brother to scout. He is almost too real for this book! If you look at it, Jem acts in ways and does things that most older brothers do to their smaller, weaker siblings; in this case a sister. Basically, he acts like he can do anything and act he wants to her. In some parts of the story, Jem is loving, kind, and gentle with the younger Scout. This is shown mostly in the beginning of "To Kill A Mockingbird." Take for example towards the time when Dill arrives. He's great before he arrives and even better when Dill just