A darby is used to ensure walls and floors are even and ready for the decorative finish.
The darby is mainly used in plastering, particularly wet plastering. Wet plastering has been somewhat replaced by the introduction of gypsum plasterboard in the 1940s, which led to drywall plastering becoming more common.
This means wet plastering, and consequently use of the darby, are speciality techniques used mainly in restoration and repairs.
Wet plastering consists of layers of plaster whereas drywall is plasterboard with a skim coating (very thin layer) of plaster.
Rendering is the same process as wet plastering but on external surfaces. It is known as stucco in the US.
The darby is used to even out lumps and bumps and create a level surface.