Although the word "Magnum" is as much a marketing label as a classification, in firearms it is generally used to denote extra-powerful ammunition and the guns which fire it. Not to be confused with overpressure or proof ammunition, which are "overloaded" standard cartridges.
The term "Magnum" became popular in the early 20th Century, and reached the high of fame when Dirty Harry hit US the silver screen carrying his legendary . 44 Magnum. In the mid 1930s, the popular .38 Special rounds became the subject of experiments in response to the new Colt .38 Super Automatic round. Colt had produced the SA by "overloading" its standard .38 ACP round, and the result was growing popular with Law Enforcement and Gangsters alike due to its ability to go through armor or cover, like cars. Smith and Wesson responded with the . 357 Magnum, a .38 Special featuring a longer cartridge packed with powder. The new round caught on, and the Magnum label was on the scene to stay.
Both Rifle and Pistol ammunition with extra powder can be labeled Magnum, but not all are. Manufacturers may use a unique label to distinguish their product, or the cartridge may predate the practice of using the Magnum label. The Colt Single Action Army famously fires .45 Colt, a long cartridge which when loaded with modern gunpowder can reach Magnum territory. The more modern .454 Casull round derived from the Colt cartridge stretches beyond even the famous .44 Magnum, but lacks the label. Standard-sized cartridges which are packed with more powder often get the "plus P" label.
To create Magnum rounds manufacturers start with an existing bullet and add a stretched casing for the cartridge, allowing them to increase the amount of gunpowder packed into the round. This increases the muzzle velocity; which in turn improves the range, penetration, and stopping power of the bullet without requiring a whole new caliber. With nearly all Magnum ammunition, this can be easily verified visually by looking at the cartridge's casing: a long case to hold more powder indicates a Magnum round. This extra length is not strictly necessary, as most cartridges can be packed more densely to achieve the same effect, but it is a customary practice which prevents Magnum ammunition from being loaded in weapons which are not rated to fire it. The longer cartridge can be easily seen, or even felt, when handled and in most cases will not fit in a weapon designed to fire only standard cartridges.
Magnum weapons are those which have been designed to fire the larger, more power Magnum ammunition. Magnum revolvers are most common, only needing an extended and strengthened chamber to fit the longer cartridges, they are relatively easy for manufacturers to produce. Owners may also use them to fire less powerful ammunition using similar cartridge diameters for sport or target practice, reducing wear and tear with ammunition also costing less to buy than the Magnum rounds. Semi-automatic pistols firing Magnum ammunition are rare, as the more powerful round requires a beefed-up mechanism and frame. The Desert Eagle and the Wildey Magnum pistols were developed solely to fire Magnum-sized ammunition. Magnum rifles are generally based on standard designs, configured for the ammunition.