Last weekend I was at a film festival which played 'Pirates Rule!' along with some other short independent films, and someone asked me to explain what I did, and I answered with something along the lines of this:
"Okay, so you have a minifigure, take a picture. Move the arm just a tiny little bit, take a picture. Move the arm another little bit, but slightly more than the last time, take a picture. Move the arm a little bit more, bump the camera, and restart the entire shot."
My usual way of explaining it is just "Lego movies" made with stop motion. I also like to draw attention to the fact that it's probably the best way to go about making an amateur film. With live action, you need all of these actors, sets, costumes, and with a low budget, you can't really do much. Where as with brickfilming, you can make a pirate island, a planet in space, or almost anything just in your room since they're relatively cheap.
