Shiny Pokémon were introduced in Pokémon GO on March 22nd 2017 as part of the special Water Festival event. Shiny Pokémon are Pokémon of a different colour to normal. During this event, it was quickly discovered that Magikarp have a chance of being Shiny. However, there are a few notes about Shiny Pokémon in this game.

First, a Shiny Pokémon is only for you. If two people capture the same Pokémon and it is Shiny for one, it will not be shiny for any other player.
In addition to this, a Shiny Pokémon will not appear as Shiny in the overworld. It will instead be normal and then appear as Shiny when you go to capture it. However, aside from Pikachu, only the lowest evolution stage of a Pokémon can be obtained as Shiny in the wild or through eggs, so for example if you find wild Magmortar or Pupitar, you can only get a shiny by obtaining a shiny Magby or Larvitar

Mega Evolution capable Pokémon and Regional Variants that evolve from non-Regional variants are exempt from this and can appear as shiny, as can Costumed Pokémon if they are of an evolution such as Kirlia. Some evolved Pokémon will also be Shiny during Ticketed events on a case by case basis.

If you go to transfer a Shiny Pokémon, you will get an additional prompt, however no other differences exist for Shiny Pokémon.