The fae are a form of nature spirit. Nature spirits are literally apart of nature, the "spirits" of trees, rocks, rivers, plants etc. It goes hand in hand with the view that there is an "angel in every grain of sand", in the view of animism, there is a spirit in everything in nature.
The history of the fae lies in the Tuatha De Danann or literally "tribe of Danu" or more specifically tribe of the gods under Danu. Many of the Irish gods and goddesses were the Tuatha De Danann. But in the mythology (and historically) there was a war. The Irish did not win this war and the "tribe" was forced to go underground. The gods and goddesses were no longer viewed as such, and they were called the hill people (sidhe). One well known form of sidhe is the beanside (banshee). But time went on and even the sidhe grew less popular. And they were then feared by the people, called "fair folk" which then became "faery folk". And the name "fae" were born.
The fae are spirits of nature from high deities like the Fae Queen Morrigan, to elves, to the tiny ones like willow wisps.