Jem and Scout were "horrified" when they watched Atticus do something they had never seen him do before during his final summation to the jury in the trial of Tom Robinson. Perhaps attempting to alter his own appearance to present himself as more of a "common man," Atticus took off his coat, loosened his tie, and unbuttoned his vest and collar. He removed his pocket watch and chain and put them on his table.
He never loosened a scrap of his clothing until he undressed at bedtime... this was the equivalent of him standing before us stark naked.
He took off his glasses, and Scout saw that he was also perspiring--and she had never seen him sweat. Atticus was not only unburdening himself of his attorney's garb, but he was about to unburden his soul before the jury. It was the closest he could come in a courtroom to standing in Tom's own shoes.
Atticus puts himself in Tom's shoes when he recreates Tom's situation during the trial. As Tom's lawyer, Atticus must recreate the alleged rape scene, and by putting himself in Tom's shoes, he realizes that Tom couldn't have raped and beated Mayella due to his crippled hand. Atticus's closing speech in defense of Tom is a clear example of how Atticus is not only able to put himself in Tom's situation but also Mayella's since he acknowledges the fact that Mayella is lonely and ignorant.