Cleft

In generative syntax, a Cleft construction can be derived from a non-cleft construction by introducing one of its elements.

Examples
Say X, in a clause having the form It be X, and by turning the rest into a relative clause. Two cleft versions of (i) are given in (ii):

(i) We saw John (ii) a It was John [who we saw e]     b It was John [that we saw e]

Link
Utrecht Lexicon of Linguistics

Reference
Smits, R.J.C. 1989. The relative and cleft constructions of the Germanic and Romance languages. Diss. KUB, Tilburg. Dordrecht: Foris.