I think if it makes you feel something. I don't mean is has to be superemotionalfullofsadfeels, I mean like it conveys an emotion, or it seems to have a story behind it or it's just so pretty it makes you go,
There are different kinds of interest. There have been films (another branch of art) which I have found an interest in the way it was shot (cinematography) but the story it was telling (the artist's message which he or she tries to communicate using the visual language) was flat.
Similarly, there are different ways to find art interesting. On a technical level, it can generate lots of interest by using technique to draw the eye towards different parts of the image as you are led across the canvas, keeping the viewer's gaze from becoming stagnant. Use of light and dark, warm and cool, shape, line, etc.
Then there's the kind that allows you to 'feel' something towards the subject. The little things that convey emotion, story and idea. Subtlety, nuance, and an understanding of your subject, etc. Often you have to be technically proficient to generate emotion as well, but technical proficiency by itself is no guarantee that you'll get the latter kind of emotional interest and investment.
There are probably more levels that interest exists on, but that's my two cents worth.
For me, the composition and colors used in a piece of art have a large impact on whether it's "cool." I like creative use of colors that fit into some sort of scheme, or contrast, or if something moves in an interesting way across the drawing. I also like interesting and dynamic poses, and original ideas that I haven't thought about much before.