Sylveon is one of the many evolutions that Eevee can become if you follow the exact steps you need to become that particular evolved form in the Pokemon games. In Pokémon Go, you have to follow similar complex steps, but these steps are different because Pokémon Go and traditional Pokémon games do not have the same items. Of the eight evolutions of Eevee, Sylveon is not available in Pokémon Go.
Sylveon is a Fairy-type Pokemon, which means it's one of the few types of Pokemon that are super effective against a Dragon-type. It first appeared Pokémon X and Yes versions set in the Kalos region. As of this writing, Pokémon Go is still featuring Pokémon from the Unova region, which has Pokémon from the Black and White versions. Sylveon will likely not be available until the Kalos region makes an official appearance.
The traditional way you turned an Eevee into a Sylveon involves you gaining High Friendship with it, which you earn by fighting with it and having it in your party. Eevee evolution into Sylveon in Pokémon Go will work differently, but it might look the same. Based on the game's current mechanics, you'll likely need to increase Eevee's buddy level and walk around with him to receive a Sylveon. This information is unconfirmed and pure speculation.
We'll update this guide when Sylveon becomes readily available in Pokémon Go. We might see its release sooner before the Kalos region becomes available. Developer Niantic has been known to release Pokémon ahead of their region's official release, such as Galarian Pokémon being available through limited-time events.