Fellow mosaic artist Eve Lynch recently posted some interesting thoughts about why art history matters, on her blog Creative Nonconformity. It is an interesting question, and one that every artist is going to have a different answer to. I believe that art history is best learned when it is absorbed, like osmosis, by simply looking. In college I had a wonderful professor - I don't remember his name - who taught an art history class in this way. He announced at the first class that grading would be a simple pass-fail, and that we would pass simply by showing up. He told us to put away our notebooks and pens, and said that he wanted us to simply look at the slides he presented, listen to his descriptions, and think about them.
I loved that class. I don't remember what any of my fellow students said about that class, but as for me, I think I absorbed more about art history in that class than in any other. Years later, often when I would see a painting or sculpture, I'd remember it from that class and how it made me feel. Learning often is most successful when there is no pressure to learn.