Breadboard ends are a method of stabilizing the ends of a tabletop to inhibit cupping induced by seasonal changes in humidity. Because the end caps must remain tightly fastened to the field of the tabletop while the top shrinks and swells periodically, the hidden joinery involved belies the simple appearance of the finished piece.
The caps on this table were the same thickness as the rest of the top and 2 1/2" wide. They were grooved to accept a 1/2" wide tongue and mortised to receive tenons another 1 1/2" in length, which allows plenty of material to prevent the securing dowel pins from shearing the tenon ends.
The ends and top were dry fitted and the pin locations marked on the tenons, then oblong holes were routed on all but the central tenon, slightly offset to put some tension on the pins and ensure a permanently tight joint. The mortises were oversized to allow for sideways movement of the tenons, again except at center.