Berdan Primer - A primer containing no internal anvil. In the Berdan system, the anvil is an integral part of the cartridge case, formed by a conical projection rising from the floor of the primer pocket, and flanked by ( normally ) twin flash holes. Berdan cases are not convenient for reloading, as depriming requires special equipment and is time-consuming. Some claim this to be more accurate, since the twin flash holes ensure more even ignition of the powder.
Boxer Primer - Primer with a 3-legged internal anvil, permitting use of a single, central flash hole in the case head. Such cases can be conveniently deprimed by means of the decapping pin in standard reloading dies.
Interestingly enough, Berdan priming was developed in the US and used almost exclusively in Europe. Boxer priming was developed in Europe and is the only priming system used in the US