Kirkjubæjarklaustur was known in olden times as "Kirkjubær" (Church Farm) and was an important farming estate. It is one of the most tongue-twisting words to pronounce of any location in Iceland. Kirkjubæjarklaustur has developed into a village, the only centre of population in the district, with about 150 inhabitants. Kirkjubæjarklaustur, often abbreviated to "Klaustur", is centrally located in the district. Roads radiate from Klaustur in many different directions and the Ring Road runs through the district. The Laki road, just west of Kirkjubæjarklaustur, leads into the highlands. The circular Landbrot / Meðalland road serves the southern part of the district. The Fjallabak roads (north and south) lead from the Ring Road into the Interior via Skaftártunga. The Álftaver road is a circular route serving Álftaver on Mýrdalssandur.
Kirkjubæjarklaustur is the only place between Vík and Höfn which offers services, including a fuel station, a bank, a post office and a supermarket. Nearby tourist attractions include the Laki craters, the Eldgjá and Skaftafell National Park. An attraction close to the village is Kirkjugólf (Church Floor), a natural pavement of basalt. These are basalt columns down in the earth, eroded and shaped by wind and waves, but only the top can be seen, and they, as the name suggests, have the appearance of a paved church floor. It is a protected natural monument. This lava formation has similar origins as the Giant's Causeway in Ireland. All these attractions contribute to the popularity of Kirkjubæjarklaustur as a stopping point for tourists.