Completive aspect refers to an aspectual form that expresses an action that has been carried out "thoroughly and to completion" (Bybee et al. 1994:318).
The term perfective aspect is very similar in meaning, but distinguished from completive by several authors (e.g. Bybee et al. 1994).
Bybee, Joan L. & Perkins, Revere & Pagliuca, William. 1994. The evolution of grammar: Tense, aspect and modality in the languages of the world. Chicago: The University of Chicago Press.