Pressure points are a martial arts skill that is necessary and effective for any martial art. Whether it's a striking art or a grappling art, they can add effectiveness to any technique. A well placed thumb while grabbing an attacker's forearm can mean the difference between them increasing their efforts to attack or them doing their best to move away from the pain. Used properly, a pressure point attack can help you set up another technique because, with practice, you know what direction they are going to move in order to attempt to get away from the pain. Knowing how your attacker is going to move even before they know is a definite advantage.
There are claims of pressure point death strikes where striking a particular point in a particular way will cause a reaction in the body, including death several hours later. I've never seen pressure points used in this way, therefore I am skeptical of those claims.
My experience with pressure points is simply to elicit a specific response to facilitate the execution of a technique. There is a lot of literature on pressure points and literally hundreds of them all over the human body. For practical martial arts purposes, there are 10 that I recommend learning and the best ways to attack them. In this article I am not going to get into the proper names or how to attack them, but I will list where they are located. There are three on the head that I would use- behind the ears, on the side of the nose, and up under the jaw bone- toward the back. Three on the torso- one that is sort of behind the collar bone, the sternum, and the rib cage under your arm about a hand width below the armpit. Three on the arms- inside of the upper arm approximately 2" above the elbow, bicep muscle off center toward the body approximately half way up the bicep, and on the lower arm also off center toward the body and a couple of inches below the elbow joint. The last one for the purposes of this article is on the thigh, the same place where you'd get a charlie horse.
These are the ones I prefer and they work well with my martial art. If your art doesn't spend much time teaching the use of pressure points, I suggest that you gain that knowledge from another source. While you are practicing them, pay attention to the involuntary reactions you and your training partner have when the pressure point is hit. Having this information and the patterns of involuntary action associated with their use can be invaluable knowledge when you're engaged in a situation that warrants their use.