Atticus knows two things - something about Scout, another thing about human nature.
First, Atticus knows that Scout is a fighter. He knows that when Scout is angry or annoyed that she will clench her fits and fight. Scout has done this in the past, and she will probably do so later. So, Atticus wants Scout to use her head instead.
Second, Atticus knows human nature. More specifically, he knows the people of Maycomb. Therefore, Atticus understands that people will begin to talk about his defending of Tom Robinson. Pressure and teasing (and worse) will certainly come to him and to his children.
In light of these two points, Atticus predicts that difficult times will come to Scout in school. When it happens, she must hold her head up high and resist the urge to fight. In other words, she should be proud that her father is doing what is right and resist proving it through force.
Here are the words of Atticus:
“Because I could never ask you to mind me again. Scout, simply by the nature of the work, every lawyer gets at least one case in his lifetime that affects him personally. This one’s mine, I guess. You might hear some ugly talk about it at school, but do one thing for me if you will: you just hold your head high and keep those fists down. No matter what anybody says to you, don’t you let ‘em get your goat. Try fighting with your head for a change... it’s a good one, even if it does resist learning.”