In this particular quotation, Atticus is using a metaphor to teach his children the importance of empathy. He himself expresses great empathy in his behavior towards other people, most notably the mean old lady Mrs. Dubose.
Most people are familiar with the expression "to walk a mile in someone else's shoes" meaning that you can only really judge someone when you put yourself in their position and when you understand their background and the circumstances in which they've grown-up and in which they live. The metaphor that Atticus uses is a variant of this. At numerous points throughout the story he impresses upon his children just how important it is for them to gain a new perspective on life if they're to evaluate others properly. This is a vital lesson as it will allow Jem and Scout to grow and develop morally as they begin the difficult transition to adolescence.