Its power lies in the slow clap's ability to sway the opinion of an entire crowd, not with words or ideas, but with the sound of two pieces of flesh slamming against each other. The slow clap generally follows the protagonist having an, "I'm just being honest for a second" moment in front of an audience. While everyone stares on horrified (everyone in movies presumably hates honesty), one person begins to clap. Somehow, that sound alone is enough to convince everyone else that, oh yeah, they also enjoyed that crazy bullshit that just happened. Gradually it swells into a massive applause as the opinion of everyone in attendance shifts 180 degrees simultaneously. The slow clap as a concept seems absurd; an entire crowd of people convinced they like something just by hearing one person clap is insulting to human intelligence. Oh, and it turns out it happens to crowds all the time.
Even the most opinionated and judgmental people in the world are susceptible to the power of group mentality. Arguably the most prominent researcher in crowd psychology, Gustave Le Bon suggested that when people come together in crowds, they start to identify with the group at large instead of as an individual. The opinions of the crowd become the opinions of each person like a mass hypnosis.
"A phenomenon of which it is easy to establish the presence but which it is not easy to explain. It must be classed among those phenomena of a hypnotic order. In a group every sentiment and act is contagious, and contagious to such a degree that an individual readily sacrifices his personal interest to the collective interest. This is an aptitude very contrary to his nature, and of which man is scarcely capable except when he makes part of a group."
In other words, every minute change in the crowd has a ripple effect on the collective conscious and can determine the thoughts and opinions of the rest of the group. While this sometimes manifests itself in riots or acts of violence, the slow clap is a decidedly more positive symptom of mob mentality. A single person clapping in a crowd can immediately trigger the same response from everyone else because they are subconsciously serving the interest of the group, until finally, everyone is in unified agreement that they love whatever just happened.
Even if they can't remember what the hell it was.