Ok, I have an odd little question.
I'm sure that I've played a number of video games with this kind of stylized 2D background, though I can't think of an good example for the life of me (I tried, promise):
Instead of a single background image, this kind of background has several 2D images stacked on top of each other. If you move a little left or right, the images shift a just a little bit accordingly. You might see a little more of one image or another, but the overall effect is to create a kind of 2D depth of vision, like a paper diorama.
That isn't the best description, but hopefully gets the memory across.
So, my question: Does this kind of background have a name?