In To Kill a Mockingbird, how does the fact of not having a mother affect Jem and Scout?

In the beginning of the novel, a few pages in, Scout directly addresses this issue.  She states of herself, "our mother died when I was two, so I never felt her absence."  So, Scout doesn't really feel that her mother dying impacted her very negatively; she didn't remember her enough to feel a loss.  However, with Jem, Scout says that she thought Jem missed their mother, and that

"he remembered her clearly, and sometimes in the middle of a game he would sigh at length, then go off and play by himself behind the car-house."

Scout feels that when he did that, he was missing his mom, and needed some time alone to think about her.

Indirectly, we see other impacts in the novel.  Aunt Alexandra constantly comments on how Jem and Scout "run wild" and need the influence of a mother in the home.  Atticus is not too concerned, since Cal has pretty much served as a replacement mother.  And, she has, to a certain extent.  Scout tells us how Cal disciplined her, taught her, and even showed her softness on occasion.  But, they didn't have that steady, loving, soft side that a mother might have provided.  Even when Aunt Alexandra moves in, it is more to reign in the kids than to show them affection and love.  So, they grow up a bit more adult than they might have been otherwise.  With only the ideal and moral Atticus to teach them, they grew up fast, with adult ideas and codes of behavior.  They also probably did have a bit more freedom to go play games and romp about than they would have without a mother; however, this fostered their creative imaginations, and helped them to lead full lives.

I hope that those thoughts get you started a bit; good luck!