Old Irish: Hill
While the term sídhe is used to refer to what we call "fairies," the word originally meant "hill." Now, sídhe refers most specifically to the Tuatha de Dannan, "The Tribe of Danu"1, the hero-gods of Ireland, who came from the four cities of Murias, Finias, Gorias, and Falias. When the Milesians arrived after the de Dannan, they drove the gods under the hollow hills, which were called sídhe. Eventually, the hills and the people became one in the minds of the Irish, who refered to them both as sídhe.
Now, what is interesting to note is that these mounds or hollow hills are often thought to also be burial mounds--barrows. This belief in the gods who live in the Hollow Hills may be the remnants of ancestor worship of an early Celtic race.
It is also worth noting that the term sídhe later passed into Welsh poetry, namely that which is attributed to Taliesin. In two poems he references a Caer Siddi--in "Prieddu Annwn" ("The Spoiling of Annwn"), and in "Kerdd Veib am Llyr" ("Song Before the Sons of Llyr"). Of the first, "Save only seven/None returned from Caer Siddi" listed along with other otherworldly cities in Annwn. The second: "Perfect is my seat in Caer Siddi/Manawyd and Pryderi know it," refering to the Mabinogion adventures of Manawyddan and his stepson Pryderi through the otherworld. It is more than likely that "Caer Siddi" refers not to a real place, but to an otherworldly place.
1. While it means "Tribe of Danu," one can make the case that it means "Tribe of the Danube
." For more, see Tuatha de Dannan