When you're viewing individual images in Lightroom's Library, Develop, or Print modules, you have the option of changing the color behind the image. Although "color" is a little generous--they're all neutral shades of gray, from white to black.
There's no right answer on which to use. Much of the time it's a matter of personal preference, although there can be times that changing the background color can be useful. For instance, when I'm doing white-background product shots, I like to change the background color in Lightroom to white so that any shadows or vignettes at the edges of the frame show up. It makes it easier to see any fixes that need addressing. Similarly, a white background might be useful for visualization if you're prepping an image for printing that you know will be framed with a white mat, or if you want to make sure that blacks are true black. My general go-to is the "dark gray" setting, but that's just a matter of preference.
Changing the background color is simple to do. Make sure you're in the Library or Develop modules. If you're in the Library module, make sure you're in the single-image view--it doesn't work with the thumbnail grid view.
Then right click in the area immediately surrounding the image. How large that area is will depend on how much you're viewed in as well as the aspect ratios of the image relative to the view window.
A small pop-up window will appear:
Here's a close-up of the menu with the available options: white, light gray, medium gray, dark gray, darker gray, and black.
The options are pretty straightforward, but here are some simple examples of the various options.
Things to Know
This setting is applying to the program's interface itself rather than individual images. So you can't assign a separate color for each individual image.
It only works in the single-image view, and only in the Library, Develop, and Print modules. When using it in the Print module, you get a drop-shadow around the edges of the virtual paper.
The only options are shades of gray. There's no color picker to choose, say, red or blue. Which makes sense for an image editing app's interface.