Bench dogs are used in conjunction with the vises as work piece clamps. A piece can be clamped to hold it in place for planning or assembly. Bench dogs and bench vises are the on a flat surface are the foundation for unplugged woodworking.
I used round dogs because round holes are easier to make than square holes. A square dog will not rotate but a round dog will diagonal clamping. Standard size is ¾ inch.
Here we have a purchased dog in the rear and a shop made wooded dog in front. The purchased dogs are usually of aluminum or brass to save plane irons from nicks. The wooded dogs are very easy to make.
Here you see a piece clamped between the end vise and a bench dog located in one of several holes. The end vise used is a single screw so clamping as shown in not advised.
The face vise has a built in dog that can be slid up for use. A set of dog holes across the bench are lined up with this vise dog. Clamping options abound.
Vises are expensive so an alternative exists. The screw dog allows you to clamp anywhere on the table.
The screw dog lets you use any dog hole as part of a clamp.
You can make wood dogs. Just cut off a section of ¾ dowel then cut a flat on the top. Cut a reverse flat and you are in business