Genetic mutations, more or less. You see, anonymous, very occasionally, the process of combining genetics during breeding doesn’t quite work out as intended. Recessive genes here or there get triggered, resulting in the abnormal production of one pigment or another, thus producing an alternate colorization you know as “shiny.” It’s very similar, in fact, to albinism or the purple kecleon phenomenon.
The reason why it’s so rare, meanwhile, is in part because it’s all determined by recessive genes. In order to produce a shiny, you must first have two parents who have the “shiny” gene, and even then, the shiny egg requires a very precise combination of their genes. Otherwise, without that perfect combination, the dominant genes for colorization will be expressed instead, resulting in a rather normal-looking pokémon. This is, of course, oversimplifying genetics, but that’s the basic gist of it.
Besides the fact that shininess is determined by an extremely precise combination of genes, it’s also not an ideal state for a pokémon to be in. With some species, an unusually colored pelt may render a specimen incapable of camouflaging properly, which could either put the entire colony in danger by calling a predator’s attention or make hunting difficult by making the predator easier to spot. In other species, the alternate colorization may be linked to other defects, such as blindness or photosensitivity (or, in the case of plant-like pokémon, an inability to photosynthesize), all of which make life difficult for the individual, rather than the colony as a whole. In either case, some species, particularly those that form small colonies in extreme environments, may take to culling oddly colored hatchlings due to any of these reasons, which increases their rarity.
In other words, shininess is really only a trait valued among domestic pokémon. The reason why it’s so rare is because of the difficulty in breeding such a specimen and the unlikelihood of its survival in the wild.
The Pokédex According to Bill 