A rabbet is formed by removing a section of wood from the edge of a board. When you place another board into this recessed section, a rabbet joint is formed.
This joint is produced when only one of the pieces has a rabbet. Traditionally, rabbet is placed on the back side of the face that is the most visible. This produces a joint that has a clean and undisturbed face, and the small amount of edge grain is only visible from the lesser-viewed side.
One option to camouflage this end grain is to add a chamfer to the edge. By making this chamfer the exact depth of the exposed end grain, the end grain is beautifully camouflaged. A stopped chamfer, as shown in the photo to the right, adds further aesthetics to the joint.
Another option to camouflage the end grain is to actually reveal more end grain! By cutting the length of the rabbet slightly shorter (by the width of the exposed end grain), the corner produced is attractive and can be emphasized with a contrasting stain or paint.
A double-rabbet joint is one in which both boards to be joined receives a rabbet. If both boards to be joined are exactly the same thickness, this type of joint can be faster and easier to produce since the rabbet is a consistant depth, and every board receives an identical rabbet.
This type of joint resembles a shiplap joint, but with the length of the rabbet being exactly 1/2 the stock's thickness.
A double-rabbet joint is one in which both boards to be joined receives a rabbet. When the two pieces are joined together, the two pieces are effectively locked together and this provides some additional strength to the joint against racking. The second rabbet does not need to be large, and even a single saw-kerf is sufficient to produce the desired strength.
This joint can also be accentuated by various end grain details to hide the separating line between end grain and face grain.