The Vulcan nerve pinch was a martial technique developed by the Vulcans. Likely related to neuropressure, it involved applying pressure near the base of the neck and nearly instantly rendered the target unconscious (often so fast that the target was unable to cry out).
In at least some cases the results resembled an extreme trauma to the trapezius nerve bundle, as if the neuro-fibers had been ruptured.
The technique did not appear to cause permanent injury and seemed to be effective on most humanoid species. The only Human to have ever been insensitive to it was Gary Seven, possibly because of metabolic alterations obtained on his planet of adoption. It was proven inefficient on robotic androids when Spock took the time to softly try it on android Alice, who simply asked him calmly if that gesture had any significance.
Spock did the Vulcan nerve pinch once to a horse, Selek did one to a Le-matya, and Tuvok once did it to a member of Species 8472 that had disguised itself as a Human. Spock was also known to use a two-handed variety of the technique to subdue two opponents.
It is unknown how this technique works across species due to the diversity of alien nervous systems. It is possible that it uses psionic energy, of which Vulcans are known to make use. However, this does not seem consistent with non-Vulcans, and in particular androids and shapeshifters, using the technique.
It was referred to as the Famous Spock Nerve Pinch or FSNP in the scripts of TOS. It was invented for the episode "The Enemy Within" by Leonard Nimoy, who felt that Spock was too dignified to render someone unconscious by striking them over the head. The first character on which it was performed was James T. Kirk.
According to Leonard Nimoy, on the "25 year mission tour" video, when he was pitching the idea for the neck pinch, the director asked about it and Nimoy said that Spock was a graduate of the Vulcan Institute of Technology where he took a number of courses on the human anatomy and that Vulcans have a kind of energy that comes off their fingertips, which when applied to certain points on the human neck, it renders the human unconscious. Nimoy said then that the director had no idea what he was talking about but then when he explained it to Shatner, he got it immediately and Nimoy credits Shatner's reaction as to what sold the idea of the neck pinch.
Oddly, Leonard McCoy was unable to use the pinch on a Federation security officer while carrying Spock's katra in Star Trek III: The Search for Spock, leading to speculation at the time that Humans did not possess sufficient strength to use it. Since it was later established that Humans can use the technique, one must assume that McCoy's confused mental state was to blame (especially given Archer was carrying Surak's katra when he performed it), or perhaps his advanced age coupled with "a touch of arthritis."