We use this expression to say that we did or are doing something because we were/are interested to know.
You can use this phrase in ………… language.
A: You weren’t in when I called yesterday. Out of curiosity, where were you?
B: Oh, yes. I was with some colleagues who I hadn’t seen for years.
A: Are you going to see Martin later?
B: Yes. Why?
A: Well, just out of curiosity, can you ask him where he got his iPhone? He said it was quite cheap.