Pokémon will evolve once a certain level is reached. The level required is the same as for the core series games. If the Pokémon usually evolves by a different method (such as by trading or Evolution stone), then the level required is set at level 36 for most Pokémon. This is except Pikachu, Clefairy and Jigglypuff, which all evolve at level 22.
Eevee also evolves when it reaches level 36. If Eevee has more Sturdy Stones than Mighty Stones attached to its Power Charm, it will evolve into Vaporeon. If Eevee has more Mighty Stones than Sturdy Stones, it will evolve into Flareon. If it has an equal number of Mighty and Sturdy Stones (or has no stones attached to its Power Charm), then it will evolve into Jolteon.