“Bench Proof” is a term used to describe an intermediate rising between the first rising (or “ferment”, during which you allow the yeast to grow numerous enough eventually to leaven the dough) and the final rising in the pan or its shaped form (called the “proof.”)
You punch down the dough after the first rising, knead it a bit (usually), then let it stand for an amount of time specified by your recipe (this is the Bench Proof stage), then punch it down again, shape it and let it rise the final time.
The bench proofing time can be anywhere from 10 to 20 minutes to up to 2 hours, depending on what you are making.
The image being captured in the term is that of the dough being set to rise on the bench (aka “work surface.”)