This is one of several common methods of grafting. The engrafted twigs are called cions, the branch on which they are placed is called the stock. The essential principle is that the inner bark, called the Cambium layer, of the cion should be brought into intimate contact with the corresponding layer of bark of the stock. Further details of grafting are shown in other pictures in this volume.
This image is from: Luther Burbank: his methods and discoveries and their practical application. Volume 3 Chapter 1