The Neko-ken is one of the many special moves in Ranma's arsenal.
Ranma is generally fearless, or so he would have others believe. However, he does suffer from one weakness that leaves him paralyzed in its presence: ailurophobia, the fear of cats.
When Ranma was young, his father tried to teach him the "Neko-ken" ("Cat Fist") technique. The training technique described the trainee being covered in fish sausage and thrown into a pit of starving cats, but that only made him afraid of them. Only then did Genma read the final page of the training book, which stated that it was "...just another technique that would only be used by a total idiot. Anyone who would teach it should have his head examined", but has stated that he fell for it completely. Genma then tried to desensitize his son by repeating the training, covering the boy in sardines, salted sardines, or fish cakes instead. His efforts only aggravated the phobia. Ranma became permanently afraid of cats; he couldn't even get near one and would usually faint if one surprised him.
The Neko-ken turned out not to be a "technique" at all, but an induced psychosis. If Ranma's fear reaches a critical point (the result of being surrounded by cats and/or unable to get away from them for an extended period of time) his mind retreats into a condition of galeanthropy, the delusion that he is a cat. This state manifests by fighting like an unrestrained wild animal, using his power more efficiently, as well as the ability to attack his surroundings with air pressure swipes powerful enough to shred trees, floorboards or water blasts. However he likely lacks ability to strategize or use signature moves. He once willingly entered the Neko-ken in order to aid him in a beachside (winter resort in the anime) fight with Cologne (for a "Phoenix Pill" that would allow him to tolerate hot water again). To do so, he tied Shampoo to his back and dashed back into the surf, turning the latter into a cat.
His "cat" mentality is territorial, playful, sleepy, and has an extremely limited attention span, easily losing interest or being distracted by a thrown stick/plaything or being drugged by catnip. However, he comes out of it after calming down/taking a nap in the lap of someone he trusts. These have included an old woman who lived in his neighborhood as a child (who according to Genma in the anime is now dead), as well as Akane, much to her embarrassment, though she seems to have gotten used to it late in the manga. Dousing him with water can also work. Ranma remembers almost nothing of what goes on while he is in Neko-ken mode, which can cause great problems if his behavior was unacceptable by human standards.
While Ranma's phobia seems to have turned slightly less drastic over the course of the manga, it does not help that Shampoo, who is obsessed with him, is cursed to turn into a cat when hit with water, or that Maomolin the "monster cat" is counted among his adversaries.