Primarily constructed with the aid of a router, lock joints are variations on dado-and-rabbet joints. Their primary use is to attach drawer fronts to sides, or in locations where one face of a case must resist being pulled away. Regardless of the construction technique, precision cuts are required to ensure this joint mates correctly, but if done correctly it offers significant strength.
Simple does not refer to the ease of construction, but refers instead to the fact that the joint resists opening in only one direction. Note that the drawer front can not be pulled off since the side holds it in place. However, this joint does not offer any special benefit to prevent the side from being pulled off, but this is not a concern in drawer construction.
Complex refers to the fact that they provide an additional dado on the front board that serves to resist the side panel from being pulled free.
Lock miter joints present the appearance of a mitered joint when viewed from the outside, but they offer the strength of a dado to resist separation.
Any of these joints can be made using a tablesaw with a dado blade and some patience, however the construction of any locking joint is greatly simplified by the use of a router table and an appropriate router bit. Once the router is setup and the bit height adjusted, one piece is passed over the bit while standing on its end grain against the fence, and the second board is passed over the bit while laying flat on the table. This will produce the two profiles that lock together.