Prof Young,
The term Magnum Primer originally means a primer for a magnum case. Magnum cases are larger than standard cases, as the name implies, so they hold more powder. Since the empty airspace in a case full of powder is the space between the grains, you can see that magnum cases will have more total empty space in them than standard case sizes do, even when the loading density is 100%. Progressive powders, especially the slower ones typically used in magnum cases, require a minimum amount of pressure to start and maintain burning. Even though they release their own oxygen during combustion, they don't release enough to burn all the fuel available from the same molecules (the reason you get unburned carbon left over in the barrel), so if they don't have adequate start pressure and temperature they don't liberate oxygen from the nitrocellulose fast enough to sustain the reaction and they can actually squib out (extinguish in the case).
So, what magnum primers did originally (and still do) is make more gas to better pressurize the larger amount of empty space in a magnum cartridge to sustain ignition. Because of the relationship between temperature and pressure, keeping pressure higher also keeps the temperature higher. This means, by the way, that in a non-magnum case that has a lot of empty space due to poor case fill by the powder charge, a magnum primer may also be provide best ignition consistency.
In 1989 CCI took the magnum primer concept a bit further. They had noticed that even with adequate pressure from a primer, the very heavy deterrent coatings on the spherical propellants developed for the military in the 1960's (sold today as HS-6, H110, H335, BL-C(2), H380, H414, U.S 869, 296, 748, 760, and still using the unchanged 1960's formulations) had such heavy deterrent coatings that they resisted ignition even with adequate pressure. So CCI added metal powder and barium oxidizer to create a very hot white spark shower that would more reliably get these powders burning. It significantly reduces muzzle velocity variation in some instances, so the recommendation came to be made that these primers should be used even in non-magnum cases when those powders are employed.
Problems with using magnum primers:
Some benchrest competitors complain that the more pressure the primer makes, the less they are controlling it with their powder charge and that increased velocity SD can result. Obviously, this applies mainly to stick powders and other easy-to-ignite powders in loads with good load density.
In very small powder spaces (the .22 Hornet is famous for this problem, as are some pistol cartridges) a magnum primer can make enough pressure to start unseating the bullet before the powder burn gets seriously underway. This can actually increase velocity SD. The way to tell is to try both magnum and standard primers with a starting load of your powder of choice and shoot them over a chronograph and then choose the primer that produces the lowest velocity SD.
Pressure can change. Due to the bullet unseating issue, magnum primers can actually reduce peak pressure in some loads. Mostly, though, it either stays about the same or goes up, as is determined by an increase in measured velocity. Typically, in cases that use large rifle primers, the difference is rather small and not enough to justify adjusting a load unless the velocity shift reduces your group size by moving you off a barrel time sweet spot. In cases using small rifle primers, you usually seem more effect from shifting from standard to magnum primers. I've seen about 11% pressure increase change in one instance in the .223 Remington.
This article is worth reading.