The karate chop is one of the more iconic motions in the art of karate, and many other Asian martial arts. The image of a karate master chopping a bad guy on the neck to make him collapse is a part of popular culture. However, what that chop actually does when it hits the side of the neck is more complex than the movies imply.
A karate chop is a hand strike where the karateka hits a target with the side of his hand, between the top of the wrist and the bottom of the pinkie. This is generally called a sword hand or knife hand by practitioners of the art. A karate chop serves two purposes as compared to a punch. It strikes with a thick chunk of muscle, rather than bone -- meaning it's less likely to harm the person doing the hitting. It also strikes with a smaller surface area, meaning more force gets imparted to the side of the neck when it lands.
The neck is an important part of your body. Like other important points, most famously your groin, it contains a disproportionate number of sensitive nerve endings. This means if you get hit on the side of the neck, it hurts much more than getting hit in the arm or chest. This pain can be enough to overwhelm somebody, especially if hit by surprise. Although the pain alone is unlikely to "take him out," it's very likely to cause a second of hesitation.
The vagus nerve is your longer cranial nerve and is responsible for carrying much of the information between your brain and body. It runs along the side of the neck. A sufficiently hard and precise chop to the area around the vagus nerve can cause disorientation, dizziness and even unconsciousness. For best effect against the vagus nerve, a chop must slice along the neck so it peels away the layer of protective muscle before hitting the vagus directly.
Along the front section of the side of a neck, you will find the carotid artery, the vessel most responsible for bringing blood to the brain. A chop there can momentarily interrupt blood flow, much like squeezing the sides of a garden hose for a moment. Since your brain relies on blood flow to operate, this interruption has many of the same effects as a hit to the vagus nerve: disorientation, dizziness and brief loss of consciousness.
An effective chop to the side of the neck is serious business. It's not likely to make your opponent crumple like in the movies, but you can use it to create a few moments of disorientation and inaction, during which you can flee the scene, or attack further to finish the confrontation. This is not something you should do to friends.