That is actually the advice for gallery owners. I should know :(.
Each time I see this subject line go by, a little voice in my head says: "It's like pornography, you'll know it when you see it." But I think for a serious answer, the one from Jovo is about as good as you're likely to get. I think 'Fine Art' might be a useful phrase to differentiate one's intentions, as in "Yes I'm a photographer, but I don't do weddings or bar mitzvahs, I'm a fine art photographer" but a rigorous, universally agreed on definition is just not likely.
What makes a fine art photograph?
Reputation of artist in the broader arts community, which also includes photographers
Quality of application of his/her skill to the subject
Visual and conceptual interpretation of the subject, which must carry through and be strikingly evident
Consistency of producing his/her work to a very, very high standard, which means nothing is done cheaply
Bespoke production of the print, whether it be in a traditional wet darkroom or analogue-digital: even a speck on a print will fail it
Production of Editions, with the first often being the most pricey, and all future editions being either identical or varied. A special customer-requested edition is serious stuff
Reputation / representation with a recognised gallery where the artist's works and biography make clear a history of long involvement in quality art production.
Fine art photographs are not a figment of the imagination, but a quite lofty achievement which takes a lot of hard work, money (lots of it!) and dedication to maintain a stable customer and thus, cash stream. If not producing the work yourself, the lab you deal with must be absolutely on top of their game and have a solid work ethic. No corners are cut, no expenses are spared and no pretentious assumptions about the quality of work are made, the work must speak for itself with little said (if anything at all) by the photographer.
Landscape photography is out of favour in art schools, and has been for 20 or more years; it's seen as backward, romantic crap. If it works at all, the photographer has been long established and has a feel for the market (and the competition), and varies his/her repertoire to cater for a discerning demographic. It's no longer enough to have the biggest large format camera, a gaggle of lenses, a wooden tripod and gung ho: it is the intellectual clout and reading/analysis of the market that puts you in your place. In the last 10 years in Australia a great many photographers involved in fine art work have left the industry or moved to digital (for corporate, advertising or weddings, where the money is plentiful for those with skill) and only a very, very small number now make a living in Australia from fine art photography, namely Ted Mead, Rob Blakers, Peter Dobré, Ken Duncan... maybe three of four others (and all the same stuff being produced), and they are using adaptive digital because the market is less patient now for analogue the "we want it now" thing is what is driving the transition to digital.
Well I like my Doctor for who she is, and we aren't married yet, but I suppose that if nothing else, she may let me have a darkroom in the basement of her nice house someday. But she certainly wouldn't let me use her money to buy equipment etc. she's made it clear that she want's someone who can support themselves and be stable-ish. So if I'm not semi-successful as a photographer soon, I'm screwed...
Whenever I encounter people who refer to themselves as "fine art photographers" I do my best to avoid them in the future, because if I subsequently see their work I very rarely consider it either fine or art.