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Woman: I didn't know you were coming back.

Man: I wasn't, but I had made an appointment at the hair salon before I left, and they don't do refunds for cancellations. I'm very cheap.

What does "I’m very cheap" mean in this conversation？

It means "I don't like to spend more than I need to". He has paid for an appointment, so (he says) he will come for his appointment, or he would have wasted the money.

cheap (adj.): unwilling to spend money

The dialogue doesn't entirely make sense, as the relationship between the two is not clear. However what the man means is that, since he would forfeit money if he missed his appointment, he decided to get his hair cut anyway. He doesn't like to waste his money.

This is a quote from the TV show, "The Marvelous Mrs. Maisel."

It is typical when complaining about someone to say, "Bob is very cheap." It's an insult and means Bob is unwilling to spend money, usually on anyone but himself. It applies in a social context, for example Bob went to a bar and didn't buy anyone but himself a drink. Or perhaps Bob never tips waiters (considered extremely rude in the US).

It would be very rare to say, "I'm very cheap." unless you were intentionally being self-deprecating as again, it's an insult.

In the show, the doctor tells Mrs. Maisel he came back to the resort because he had a haircut scheduled and is too cheap to pay for it and not get his hair cut. He's not. In fact he probably doesn't even have a haircut scheduled. It's a tongue-in-cheek/disguised way to say he really came back to see her, and she understands that. That he said it with a smile is another indicator of how it's typically used, i.e. in this context he is flirting with her and definitely not complaining or making a true statement about himself.