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Sylveon is one of the many Eevee evolutions and holds the distinction of being the first recognized Fairy Type. It was thanks to the first Sylveon that the mystery of the Jigglypuff, Snubull, and Clefairy line's mysterious resistance to Dragons was officially solved(1). Fairy Type is now an established if poorly understood type(2).
(1)(2) See: Fairy Type: History
Sylveon is a difficult Pokemon to acquire, as their numbers in the wild are extremely low and they evolve from the already elusive Eevee. Sylveon evolves from Eevee using a high concentration of internal Fairy energy (normally knowing a Fairy technique is enough) and a powerful bond with a human as a catalyst. The resulting Pokemon is a varied powerhouse with the ability to easily bring Dragons low, causing much disruption to many high-level trainers who depend on Dragon Types.
Like most Fairy Types, Sylveon is a very social pokemon and needs frequent contact with either people or other Pokemon to maintain optimal health. For this reason, it's recommended to have Sylveon out if it's pokeball for training/playtime for at least several hours per day.
The ribbon-like 'feelers' on Sylveon act as focal points for Fairy energy, and on contact, Sylveon can use empathic abilities to read it's targets emotions and intentions, and even relay it's own emotions to the target. An experienced Sylveon can use these same abilities remotely just by pointing it's feelers at the target.
Sylveon is one of the few pokemon that would not exist without human interference, and such issues show with the difficult art of breeding them. Sylveon has a very irregular mating cycle triggered only by reading strong human emotions of affection. This oftentimes leaves the pokemon pining for their trainer with little interest in suitable breeding partners. This has spurred discontent among pokemon rights activists from the implied message that the Sylveon are being forced to breed against their will, but Pokemon League investigators have found no such evidence among licensed breeders.
Getting a Sylveon to shift its affections away from its trainer to another pokemon is a time-consuming endeavor that has no guarantee to work, but successful cases have produced Eevees well above market price just from the rarity of the Sylveon mother's lineage. A purebred Eevee produced by two purebred Sylveon parents can easily fetch twice their already high market price. It is currently unknown if the Sylveon lineage gives the resulting Eevee a predisposition to evolve into another Sylveon or learn Fairy techniques. Considering the phenomena has been recorded in Eevees borne to other parents, it is likely, however.