It means, think what it is like to be me.
Ok, say I said I disagreed with a friend's decision, pretend that she denied her father some alcohol.
I might say, "oh come on, he's old enough to make his own decisions!!!"
She might then say, "yes but he's got a liver problem, put yourself in my shoes! Would you give your dad some alcohol when you knew it was bad for him?".
It means, please consider me, my thoughts, my decision, understand why I am doing/saying what I am doing/saying.