The following versions exist with regards to the naming of the village:

• According to the first version, the name of the village, Kritou Terra, is linked to the uniqueness of the village as far the type of the carved caves is concerned. In particular, the word “Kritou” derives from the Frankish word “la grotte” which means caves, whereas the word Terra derives from the Latin word “terra” which means earth.
• The second version refers to the name of a fief owner named Erotokritos. According to this version, the name Erotokritos and the word Terra led to the creation of the present naming of the village. This version is supported by a copy of an old document that the Community Council has in its records and which has been retrieved by the website: 
  www.hellenica.de/Griechenland/Zypern/GR/KritouTerra.html. 
  Cited below is a part of the aforementioned document:

According to the above excerpt, the village was named after the Greek phrase “stou (Eroto)kritou” which was then changed into a female name. The addition of the word Terra, as the above excerpt explains, is linked to the expansion of the village which resulted from the unification of the village of (Eroto)kritou with the neighbouring village called Terra. What is worth mentioning is the fact that researchers do not seem to agree, since some of them consider this version to be the prevailing one, whereas others consider it as the least probable one. According to the latter, however, this version of the naming is more linked to the naming of the community of Kritou Marottou.  

Sources: 
Kritou Terra Community Council 
www. hellenica.de/Griechenland/Zypern/GR/KritouTerra.html
Great Cyprus Encyclopaedia 
Dr Christou G. Aristeidou
Savvas Arkadiou