When you ask “What does [it] mean to you?” with genuine curiosity, you are seeking to get to know the other person a bit better. People can have varied thoughts and feelings about the same situation or experience. Similarly, words have different connotations for different people.
“What does that award mean to you?” “What does ‘fun’ mean to you?” “What does having your family come to the party mean to you?”
By asking them to share what that experience or words mean to them, you are asking to be invited into their thoughts about that experience. Then, from that place of better understanding, you can better gauge how to respond.