“Put yourself in someone else's shoes.” isidiom that means if you imagine yourself to be in another person's position, good or bad, you may understand how they feel, good or bad, or why they have done they've done.
This idiom comes from the facta pair of perfectly fitting shoes for someone may not fit another person as perfectly. So, literally, only if you put another person's shoes can you feel how it is to walk in．
Metaphorically speaking, “their shoes” stands for other people's position. A local boy is detained(扣留) by the policea theft, and one of his friends might(private) say to himself: “I wouldn't want to be in his shoes now.” That is, he doesn't want(put) into prison for stealing.
By trying to “put on their shoes”, we try to imagine ourselves insituation, by seeing things from their point of view, by thinking about how we would want to be treated if we were them.
Harper Lee, of course, (express) this idea best in To Kill a Mockingbird: “You never really understand a person until you consider things from his point of view—until you climb inside of his skin and walk around in it.”