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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？

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.

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.

[Edit] As others have mentioned, "cheap" has negative connotations. The positive synonym is "frugal". It's unlikely anyone would call themselves "cheap" except perhaps to poke fun at some character trait:

I was going to buy that laptop I've been wanting for a while, but $25 for shipping is just too much. Go ahead, say it -- yeah, I'm a cheap bastard.

In this context the man does not have an appointment; rather he has invented a story to explain why he came back to see the woman. I expect it's meant to make her laugh at his self-deprecating humor.

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

Not everyone is ashamed of admitting their overly frugal nature.
I know people who like the challenge of driving costs down as
much as humanly possible - and thus freely (and proudly)
admit to doing so. – Flater

I agree with Flater: I have known all sorts of people - poor, middle-class, and rich people too -- who are extremely proud of how "cheap" they are! It is not considered an insult to them when you speak of them in such a way. However, you would not want to assume that someone wants to be called "cheap" when a less offensive word would be "frugal."

"Frugal," at some point in the long distant past was considered by the Romans to be a Very Good thing (see "frugal" entry at etymology.com for interesting notes about the word's long-ago origins in the Latin language).

However, as recent as 40 years ago it was not considered such a good thing by most of the people I knew during my childhood. My family's guess as to why, was that in the aftermath of the Great Depression in the U.S. (which my grandparents lived through as "poor people"), no one wanted to be poor, and poor people were forced to continue living frugally for many years, so no one wanted to be frugal because it was a sign that they were not very successful in recovering from the financial crisis.

So during that time, poor people in our area (not sure if this was true all over the country) often referred to their most frugal friends or relatives as "smart"... not that they were very intelligent, nor were they well-schooled, nor were they good readers, nor were they very well dressed... these were farmers who kept their kids out of school to work on the farm quite often. To them, "smart" meant the same thing as we would mean today if we said that a person is "frugal" and "hardworking"... but again, see that link about the Latin roots of this word "frugal," it originally had a lot to do with how hard someone worked, as well as their good choices in spending their money.

This apparent distaste for the word "frugal" was reflected in "The Frugal Gourmet," a tv show that aired starting in 1983. The show's host used to defend the word "frugal" and "remind his audience that frugal doesn't mean cheap," according to imdb.com. The host would have probably said that being frugal means not wasting money so that you have more money to spend on extremely good food.

It is amazing to me how events that shaped our history, sometimes had a powerful effect on language and what was appropriate or inappropriate to call someone. And oh, what power is held in the hands of tv hosts, even to change our perception of our language and its words! I hope this is helpful.

Oh, and par mentioned the original quote about being "cheap" came from a tv show called The Marvelous Mrs. Maisel. I looked that show up on imdb.com because I have never seen it, but the quote makes sense in more than one way, given the show's subject matter.

It is about a Jewish lady in the 1950s who wants to become successful. Jewish people are not always cheap or frugal, but in the 1950s a lot of people assumed that was true. So for a tv show set in the 1950s, it makes sense that this guy who makes the comment to the beautiful lady, is interested in her.

He was not necessarily serious that he is "cheap," but he thinks, because of his perception of her being a stereotypical Jewish person, that she would appreciate how "cheap" he behaved in coming back for his appointment. I doubt the guy actually had a hair appointment! This may have all been a part of a pickup scheme where he is interested in her romantically.

I can't find a good source that goes into depth about the history of antisemitism, but if you search on "American Jewry in the 1950's," what is returned is a nice article written about the challenges faced by the Jewish people in America prior to 1950. So 1950, the time period in which the Mrs. Maisel tv show is set, was a turning point maybe, in the history of Jewish Americans. Not sure that is a good explanation for why the doctor referred to himself as cheap, but I hope it does shed some light.

Rabbi Salomon, in his video "Cheap Jews!" on aish.com, gives a cute short talk about how he is proud to be a "cheap Jew" if that means being frugal. He gives the example of a rubber band he found on the ground, picked up, and brought home to use, as he often does with rubber bands he finds laying around. My family have Jewish roots, and we have always been quite proud of our thriftiness too! So some guy who made a romantic pass at me by pointing out how cheap he is, would make me laugh, especially if he was NOT Jewish and it was obvious to me that he was desperate to get my affections.

I looked at a lot of articles which claimed to explain the difference between "frugal" and "cheap," and this was my favorite one. It even mentions a tv show on TLC called "Extreme Cheapskates" which I hope to see an episode.
https://freefrombroke.com/frugal-vs-cheap/

Thanks for the interesting topic and all the responses, I am brand new here and I probably won't make a post again. You might still be reading this one 20 years from now, ha! Sorry for the long post.