"What is art?" is not unlike the question: "What is beauty?", books have been written about it and the discussion, I'm sure, will continue long after we're dead.
A question I've pondered lately:
Is art primarily commmunication, or personal expression? Can it be one and not the other? Is it necessary to have one, both- or neither?
e.g. Pollock's art seems to be pure expression, more about the act of creation, the dance, than the art-object resulting from the act of creation. In this way it seems like one of the few instances where visual art approaches the purity of music, and one can imagine Pollock in the same sort of trance-state Jimi Hendrix appears to slip into when he's knee-deep in a jam session.
On the other hand, there's the communicative function, who absolutely requires the art-object, and which the majority of the plastic arts seem to give a strong emphasis. The extreme I suppose would be something like the didactic Christian art of the Medieval period, back when the artist was more craftsman than prophet. But I've also wondered if all plastic art doesn't inherently communicate something simply by virtue of existing (so the artist should be aware that the act of perception will force his art to communicate to a viewer regardless, and thus should be mindful of what his art will say).
Maybe it's all about the function you want your art to fill. Art seems an umbrella term for a thousand different things anyway, so maybe it's a matter of semantics.