Excellent and detailed link Dunner. It explains the two in greater detail and has pictures too, ChuckD.
"Boxer" primers are the most commonly used commercial priming system. The primers itself has a cup and "anvil" and the primer pocket in the case has one flash hole in the center of the pocket. This makes it easy to punch out the old primer with a simple pin punch.
"Berdan" primers do not use the "anvil", it is formed into the case head and thus there are two flash holes on either side of the anvil. This makes the Berdan much harder to reload.