If you're referring to set construction, I believe what
you're asking about is an exact scale model of the
stage and/or the set built entirely out of poster board
and foam core board.

Foam core is approx 1/8" thick, and if using it to
construct the walls of your model, it will be
comparable to the fat side of standard 2"x4" (or 3
1/2") This gives you a scale model of approx 1/2" = 1
foot.

It is not painted (hence the term "white") but is used
primarily for directors and other designers as a 3-D
rendering of the space to help visualize movement
and give them a better idea of entrances, exits,
usuable wing-space, sight-lines, heights of
platforms, steps, etc.