What is the term for the big background that the canvas lies on in Photoshop?

Photoshop CC has helped us define terms that were already used in illustrator before. It's not all set in stone, as Johannes was saying, but the "image" as you called it is now called an artboard.

That being said, I don't like calling the background area the "document window" because "window" has a connotation of the entire application.

Final answer: The background area behind the artboard should either be called Canvas or Canvas Background.

You can see the canvas can actually be painted on, and sits on what I further dubbed the cavas background.

Alex's answer is kind of right, but the area specifically is called the canvas and the canvas makes up the document window. You can see this when you are choosing a custom color for it, Photoshop calls it the Custom Canvas Color -- though I'll be the first to admit that it's kind of a misleading name considering the image itself also can be called a canvas. Sometimes people specify by calling the area extending beyond the image the background canvas.

You can see people refer to it as such as well when you google how to change the canvas background color and here's one from the Photo SE

EDIT

Since there seems to be some confusion, the term Photoshop chose is "Canvas" but because the image area itself can be, and sometimes is referred to as a canvas, saying "Background canvas" is more appropriate.