Hey Elena. It just means "see it from my point of view" or "imagine what I feel/go through". Depending on the context, the speaker is asking you to take their position to evaluate a situation.

Maybe in this contest, you might say: METTITI NEI MIEI PANNI!!!!

поставь себя на моё место

It´s when you, in an imaginary situation take the same position of the person asked you to put yourself in his/her shoes. For example if he/she is sick, you have to imagine that you are sick too and what you do, did or will do been sick.

Not to be apathetic!