As throttlekitty says it's just extra space and for game models you will only really care about the upper right part. In VFX they use UDIMS which go off the 0-1 space but we don't typically use those. As for your questions on materials, no they're handle on a polygon object basis not specifically a UV basis. Picture a…
On top of all the great explanations above, I would add that one way to understand this seemingly "unused space" is to force oneself to *not* rely on too many analogies when trying to understand any CG topic. For instance : when starting out with UV mapping/unwrapping, you might have heard things like "imagine an orange…
The area in the upper right is known as the 0-1 space: the grid starts at 0,0, and ends at 1,1 in the upper right. The rest is extra space. If you do View>Grid [options], you'll find that you can expand it as much as you want. It's helpful for a lot of workflows to visualize the grid, such as tiled textures on very large…