CP is the abbreviation of Complementizer Phrase. In generative syntax, CP is the maximal projection of COMP (C0). CP is in part an reconstruction in X-bar theory of the categoryp S' (or S-bar).
Thus the (anomalous) structure generated in (i) (see Chomsky 1981) is replaced by the X-bar structure generated in (ii) (see Chomsky 1986b).
(i) S' --> COMP S
(ii) a CP --> spec,CP C'
b C' --> C IP
Under (i) COMP contains both wh-phrases and the complementizer; under (ii) C is the complementizer position, and spec,CP the position of the wh-phrases.
Utrecht Lexicon of Linguistics