Boxer primers are what we consider "regular" primers.
There are two types of primers, Boxer and Berdan, both named for the gentlemen who invented them. Mr. Boxer was an Englishman, and Mr. Berdan was an American, but Europe adopted the Berdan priming system and the U.S. adopted the Boxer priming system.
The difference between the two, other that physical sizes, are the way in which they're constructed. Both use a primer pocket, but the Boxer pocket is just a hole in the base of the case, with a single flash hole in the middle for the flame to ignite the powder. There is the primer cup, which contains the priming compound, and an anvil is pressed into the actual primer cup, making it self contained.
Berdan primers also have a primer pocket, but the anvil is formed inside the pocket and is part of the case, not the primer. The priming compound is placed into the cup at the factory, and when the primer is seated, the anvil in the case is in the proper location to detonate the compound.
It's the actual smashing of the compound between the cup and the anvil that sets the primer off. This is a controlled explosion, whereas the gunpowder actually burns, rather than exploding. The burning of the gunpowder is what causes the gases which propel the bullet down the bore.
Hope this helps.
Fred