Fey (synonyms: 'the fey', 'faerie', 'fairy' 'fae', etc.) is a catch-all term for the magical non-humans inhabiting the various planes of existence, not including gods/deities. There are several species, affiliations and cultures of fey.
The fey largely inhabit a plane of reality known varyingly as the Otherworld, Faerieland, or various culture-specific names such as Tir na N’Og. (Importantly, the faerie realm is a separate land from the Medium - also known as the Dreamworld.) This world is closely entwined with the human world, and certain liminal spaces such as caves indicate where the fabric between the worlds is thin. Liminal spaces are also sometimes manmade - henges and hedge mazes are common examples.
Only fey can cross at will between the human world and Faerieland. Humans, even elementals, need a door or to travel with a faerie.
Fae are generally divided into three very broad political affiliations. These affiliations originate from Celtic culture; the Celtic-Germanic culture is the most dominant in the fae world, and as such, demand allegiance to one or the other of the courts at risk of being labelled a troublemaker.