Shiny Pokemon are special Pokemon that have a different look to normal Pokemon. The only difference is the coloring; shiny Pokemon are not more powerful. Some shinies are a completely different color to normal, while some only have small coloring changes. Shiny Pokemon are extremely rare - every time you encounter a Pokemon there is a 1 in 8192 chance it will be shiny. See this Pokebase question for more information.
This is the complete shinydex
for Generation V (up to Black & White), which shows the shiny version of the 649 Pokemon discovered so far. You can hover your mouse over each sprite to see the normal, non-shiny sprite and compare.
See also: regular Pokedex or Pokedex with stats