Kevin is a sweet-looking guy who on the surface appears normal, but underneath is a psychotic killer who dismembers people.
He is summoned by a film strip, if someone plays the film.
He is not seen during the Purge, but he is in one of the deleted scenes. In the novelization, Kevin is described as a quiet, normal-looking person with a small smile on his face who calmly walks through the post-Purge chaos until he comes across an injured guard. He then proceeds to "exsanguinate him in a second." When Dana finds the guard, he appears "untarnished, but Dana had never seen 'anyone more dead.'" Due to his unremarkable appearance, any normal looking human seen in the purge could be Kevin.
Kevin may be a reference to Sin City's Kevin, who fits the same description. A popular Canadian cartoon called Kevin Spencer also exists. The show takes place around Kevin and his alcoholic, sociopath antics.
Director's comments reveal it is most like the character "Kevin" from the novel "We Need to Talk About Kevin", in which the child Kevin displays sadistic violent tendencies.
The fact that Kevin is summoned by a film strip may have been inspired by the character Patrick Bateman, from American Psycho. Bateman uses the excuse, "I have to return some videotapes", to leave a social situation and follow up with going on a murder spree.
It is possible he was inspired by the Juggernaut from 13 ghosts, as both were serial killers who would dismember people, the Juggernaut being mentally insane while Kevin was psychotic.