
1) Townland of County Cavan 
Found on 
https://www.crosswordclues.com/clue/burren
 [barony]
[barony]  The Barony of Burren is a geographical division of County Clare, Ireland, that in turn is divided into civil parishes. It covers a large part of the Burren. ==Legal context== Baronies were created after the Norman invasion of Ireland as divisions of counties and were used the administration of justice and the raising of revenue. Wh...
Found on 
http://en.wikipedia.org/wiki/Burren_(barony)

(from the article `Clare`) West Clare comprises plateaus and lowlands. The Burren is a distinctive region of almost horizontal limestone slabs and little vegetation; along the ... ...karst areas. The karst of Wales contains the longest caves in England, while the Yorkshire karst has complex vertical caves. Many parts of Ireland ... [...
Found on 
http://www.britannica.com/eb/a-z/b/133

Burren is a cultivated variety of potato.
Found on 
http://www.probertencyclopaedia.com/browse/QB.HTM
  No exact match found.