A technique used in (mostly) older
sprite-based video games to conserve video memory and
cartridge space, and also to keep the artists from having to draw too many graphics.
Basically, every pixel on a sprite is a number, and each of those numbers corresponds to a color on that sprite's palette. If you want to change every instance of a particular color on a sprite, you just attatch a different palette to it, with the new color at the value the old color used to be at. Voila. That graphic can now be reused for something else. Like a harder version of the same monster.
That explanation is a complete bastardization, but I'm not a programmer and I'm trying to keep it simple.
Examples of palette swapping: Scorpion, Sub-Zero, and Reptile in the Mortal Kombat series; the red and green Koopa Troopas (turtles), and Mario himself with and without flower power, in the Super Mario Brothers series; Link's different armors and swords in the Legend of Zelda series; virtually every enemy in any 2/3 view beat-'em-up (like Final Fight, Teenage Mutant Ninja Turtles: The Arcade Game, Streets of Rage); alternate costumes in fighting games (like the Street Fighter series, the Samurai Showdown series, the King of Fighters series); many of the enemies in the Diablo series.
I suppose the modern equivalent would be re-skinning a 3d model; a few games with skeletal animation systems (like Tekken Tag and Quake III Arena) will even take a new model and just reuse the old animations. Both of these techniques are infinitely cooler, more satisfying, and less cheap feeling than palette swapping.