From a conversation with Brooks Jensen from Lenswork publishing.

I know precisely what you mean, but to paraphrase those great words of St. Augustine, I know what it is but I can't explain it. Fine art photography is a burdensome term, but it does seem to have some practical use in spite of the fact that it's definition is imprecise. Although I'm sure the following will be incomplete, here are at least the ways in which I use the term:
• Photography that is personally directed, not pursued as an assignment or at the behest of others.
• Photographs that are made because we somehow feel we're doing something important, not just something that is fun — although fun is usually a concomitant ingredient.
• Photographs that we would make even if there were no hope of an eventual audience.
• Photographs for which we expect no compensation other than the emotional and intellectual reward of having made them — but for which we will gladly cash the check should someone be willing to purchase them as artwork.
• Photographs that we hope leave some indication of our having been on this earth for a short period of time once we have left it.
• Photographs that we hope that offer something of meaning and importance to our audience, whoever or whatever its size. That is to say, we hope are photographs connect with people on a more meaningful level than merely pictures. This may perhaps be the most difficult part of my thoughts about photography, but it seems to me to offer the potential to allow us to connect to one another and to break that inevitable pattern that brings us into and out of this world as solitary, isolated individuals. As such, it is the use of photography that goes beyond the mere presentation of the subject and begins to make connections between us about how we think and feel about the subject photographed.
As I say, I'm sure this is not an exhaustive list and perhaps not even very satisfying. Nonetheless, these are the ideas that occur to me about how I use the term fine art photography in an attempt to differentiate it from all the other kinds of photography that are possible.