Boxer (after Col. Edward Boxer of Britain) uses a primer that has an anvil integral with the primer itself, with a single central flash hole located in the center of the primer pocket.
Berdan (after Col. Hiram Berdan, of the United States) uses a primer without the anvil -- the anvil is actually part of the casing. Because of this, the Berdan cartridge usually has two (I've also seen one and three) flasholes located to the sides of the primer pocket.
Because the flash holes in Berdan cases aren't in the center, it's a LOT more time consuming to reload these case because the primer has to be either pried out with a special hand tool or ejected hydraulically.
Becase of this, Boxer ammo is a LOT more loader-friendly.
Now, where it can REALLY matter to you if you don't reload is with foreign military suplus ammunition, which is probably the most common form of Berdan primed ammo now available.
A lot of this foreign military ammo has corrosive primers, meaning that it can cause rusting of your gun if you don't clean soon after firing.
CCI is also making Berdan primed ammo as part of their aluminum-cased Blazer line. It's Berdan primed specifically to keep people from reloading it.
