FaerieElves in Aman as known in Westron in the folklore of the Hobbits. It is possible that it referred to what is known as Eldamar (translated as 'Elvenhome', 'Elvenland' or 'Elvenesse').
The idea of Faerie actually encapsulates a much more profound notion explored by Tolkien in his lecture and essay On Fairy-Stories, where it represents a realm on the edge of human experience in which fantastical creatures dwell.
The name 'Faerie' belongs to an early period of Tolkien's writings, and is never seen in The Lord of the Rings, but it does survive in a single usage in the earlier book The Hobbit where this high idea takes on a more concrete form, and there it relates specifically to the realms occupied by the Elves beyond the Great Sea.
 See also