This might be a better question for /r/Anthropology. This is a pre-history question. Clapping or applauding has likely been used as a way of showing approval or joy since our earliest human ancestors emerged. Primates applause (making noise through various means such as clapping, snapping, stomping, etc) to communicate, to get attention, and when pleased or frightened. There is no recorded history of the "conception" of applause, as far as I'm aware. Applause is ubiquitous in humanity's cultures and throughout recorded history.

A better question might be "what is the history of applause" in a particular culture. The Romans for example, used different methods of applause to communicate degrees of approval or disapproval.