Basics.
The Fairy-type is one of 18 Pokemon types, and the most recently-recognized typing of the 18. Recognition began around 2013, with multiple Pokemon and moves being reclassified as Fairy-type. For more information on this, please see the "History" section.
Fairy-type moves are super-effective against Dark-, Dragon- and Fighting-type Pokemon. Fairy-type Pokemon, in turn, hold weaknesses to Poison- and Steel-type moves. They are completely immune to Dragon-type damage. On average, Fairy-types tend to have Special Attack and Special Defense as their best stats, and have the highest average Special Defense of all types. As-of my time writing this, it is the second-rarest Pokemon typing overall, after Ice.
Pop culturally-speaking, the Fairy-type is often associated with, of course, fairies, as well as the color pink, young girls and queer men. In some regions, someone may indirectly ask if a man is queer by asking if he has a particular interest in the Fairy-typing. Fairy-types are also often associated with cute or aesthetically-pleasing appearances, although traditionally "ugly" Fairy-types do exist.
Notable Fairy-type experts include Gym Leader Valerie of Kalos, Trial Captain Mina of Alola, retired Gym Leader Opal of Galar, and myself (Gym Leader Bede of Galar).