Ice appears white because it reflects a full spectrum of human-visible light. It’s actually the air trapped between the ice crystals (by falling snow, generally) that does the reflecting, though. Over time, pockets of air that were trapped in the ice work themselves out. Once they do, most light has nothing to reflect off of. However, blue light has enough energy to make it deeper into the ice structure and either reflect off an internal surface or the water. Which makes this old, super compressed ice look blue.
More info than you possibly want to know about this phenomenon is available here. (Thanks Elena for doing the research on this one!)
tl;dr: Blue ice is really old ice, and here are some pictures of it.