It’s a piece of wood, usually hardwood (such as maple ) used by tailors (duh) to get flat, crisp seams or creases. It is usually rounded at both ends and has often grooves along the longer sides so you can hold it easily.
The tailor's clapper originated in the dressmaking world and was and still is used for nice flat seams without getting shiny from ironing.
Imagine a pair of pants in a delicate material, let’s say silk. Now you iron the side seams, the result will be a seam allowance that shines through and an outside seam that's shiny too. This is every dressmakers nightmare.