Fairy-type Pokémon are mostly cute, pink or feminine in appearance, and can be really powerful. Fairy types also have some magical appeal to them. As opposed to Psychic-type Pokémon, Fairy-type Pokémon have powers related to magic and supernatural powers, instead of mind power.
The only known famous Fairy-type Pokémon Trainer is Valerie, the sixth Gym Leader of the Kalos region.
They're weak against the Steel type because according to European traditions, fairies were killed with iron due to it being manmade and manufactured, which is opposite to the natural affinity of fairies. Also, in some stories fairies could not touch steel because it burned them when touched.
They're weak against the Poison type because fairies represent purity and poison the pollution. Also in some stories, villains gave fairies poison to make them grow weak.
They're strong against the Dragon type because in mythology, fairies' magic could dominate oriental dragons, even though in European legends, the dragons were immune to magic.
They're strong against the Dark type because fairies represent light and the darkness disappears with light. Also, fairies represent goodness, and this always wins against evil.
They're strong against the Fighting type because physical strength can't do anything against magic.
They resist the Bug type because in pop culture, fairies live along insects and bugs.
The Fire type resists them because traditionally fairies live in forests, and fire can easily destroy these.