There are hundreds upon hundreds of little rooms exactly like this one throughout the Amber Rust Hive, and similar rooms are common in other hives, though the specifics differ.

The primary purpose of these rooms is to provide space for shedding the exoskeleton that's out of the way of foot traffic. That frame on the wall is for holding onto during the molt, and afterward the shed skeleton is placed in one of the drawers below the comb there where they will be retrieved by the cleaners to be examined and either recycled or discarded.

That's not the only thing the rooms are used for though. The combs in these rooms are often full of whatever odd object a bee wanted to keep and there's a table embedded in the floor that can be lifted out for whatever social purpose needs a table.

Drawn with the GIMP.