A hole saw is a cup-shaped bit with teeth around the rim, which is fitted to the drill with a pilot bit in the centre and cuts large diameter round holes. There are hole saws for wood, for metal and for masonry, each with its own teeth.
In locksmithing it is used to cut the opening in the door leaf for a lock cylinder, the recess for a bolt or a rim lock, the hole for a door viewer or the housing for an escutcheon. With a good hole saw the hole comes out clean and exactly the right diameter, without splintering the wood or distorting the metal.
A badly cut hole leaves play and the cylinder or the escutcheon ends up loose, which is exactly what you do not want on a front door. It is one of the tools used when fitting security bolts.