What does 'Put yourself into the other person's shoes' mean?

This is a metaphorical way of asking you to understand another person's viewpoint. In other Words, ask yourself how things appear from another person's perspective.
It means to imagine how they feel and what their reasons are. Being able to see things from someone else's viewpoint is one of the things that mature people do, so there are a lot of idioms about this - walk a mile in someone's shoes is another one.
To put yourself in the other person's shoes is to imagine that you have their life, temporarily. You are trying to imagine what they must be going through.
imagining to put yourself in other persons position (e.g to realize the situation or to face or answer something)