Shiny Pokémon are special Pokémon that have a different look to normal Pokémon. The only difference is the coloring; shiny Pokémon are not more powerful. Some shinies are a completely different color to normal, while some only have small coloring changes. Shiny Pokémon are extremely rare - every time you encounter a Pokémon there is a 1 in 4096 chance it will be shiny (1/8192 in Generations 1-5). See this Pokébase question for more information.
This is the complete
shinydex for Generation 7 (up to Sun/Moon/Ultra Sun/Ultra Moon/Let's Go Pikachu/Let's Go Eevee),
which shows the shiny version of the 807 Pokémon discovered so far. You can hover your mouse over each sprite to see the
normal, non-shiny sprite and compare.