In traditional animation, a background layout is the line drawing of the background for a scene. It is not the finished background painted in color that you see on the screen.
Layouts are drawn from storyboards which define the action and perspective in the scene. Because storyboard artists draw backgrounds in a rough, simplified style, background layout artists take them to the next level by defining the detail and perspective. Layout drawings are then given to the background painters to color and complete the visual style.
Depending upon the style of the film or show, the lines of the layout drawings may be visible in the finished background that is used in a final production. Or the visual style may be void of line work, thus the layouts serve as a guide for the painters.
Depending upon the production, background layout artists also do background design. This is standard in television animation, which is my field, and the position is often titled background designer. The designer must envision new locations when they are called for in a script, taking into account the action of the characters and the mood of the scene. The design drawings are given to the storyboard artists to show them what a place looks like.
I often get asked what I do in animation since people outside of the industry are unfamiliar with the process. It's a lot more fun than this dry explanation of the job. A lot of creativity goes into making places that are believable in the world of the characters.
Most importantly, backgrounds must support the narrative of the story. Designers take into account things like the personal style of characters or the economic state of imaginary neighborhoods. They draw places that have history, like showing what has happened previously in a location, even if we never saw it happen, or the history of a place long before the characters existed. Even when imaginations dream up incredible fantasy worlds, places often have facets that make them relatable to our everyday world.
More than just drawing places background layout is work layered with complexities. That's what makes it so fun!
2015 Update: As my career shifts, I've been doing more storyboarding than background design.