For the “mass audience”, if someone says something you don’t like, you might boo, or shout “no”. For the “enlightened”, snapping fingers in front of their face is the way to express it (maybe derived from upper class finger snapping at servant class). Mass finger snapping is the way of engaging the group-think of an “enlightened” group of people and signaling their disrespect of the speaker.
Finger snapping is also a form of applause, especially in small venues where clapping would be too noisy; audiences are requested to finger snap as a sign of approval.
It is also an answer to the philosophical question, “What is the sound of one hand clapping?”