Most athletes and fitness enthusiasts alike are not maximizing their performance because they haven't learned to relax while under pressure or in pain or extreme discomfort. While most have heard they need to relax, I think few understand why, and even fewer master the practice.
A well known concept in Sport Psychology is the idea of Optimal Arousal. This means to acheive your best performance your arousal level must not be too high, or too low. Think of the two extreme levels of arousal. Low end arousal would be dosing off on the couch in front of a boring television program. The high end would be running from a bear in hot pursuit. Would either of those extremes be good states for shooting free throws? Of course not. Optimal arousal for almost all activities is somewhere in the middle.
One of the main reasons extremely high arousal is not good for maximising performance is because you cannot relax when being chased by bears. Relaxation is important for maximising any kind of perfomance. Think of the best musicians, the best public speakers, the best lovers; they are all relaxed. Think of more mundane activities like driving. The best drivers are alert and relaxed, not stiff and scared or enraged. Like these examples the best athletes have learned to relax when the going gets tough.
Being relaxed allows you to make good decisions. It allows you to maximise mechanical energy, and minimise muscle stiffness and nervous movements, which makes you more efficient with your own energy stores and movements. Finally it just makes the whole experience more enjoyable. When you combine all of those things it can completely change your workout or competition experience. You'll be able to better execute skilled movements, and do so more consistently, faster and more powerfully. You'll also be able to sustain high work rates for longer which means improved endurance and stamina.
While there is so much upside to relaxation it is much easier said than done. Like any other skill it requires practice to learn. My advice is to focus on breathing or some sort of relaxing imagery or repeated mantra. Be aware of problem spots where you hold tension such as the hands, face, neck and shoulders. You should be able to puff out your cheeks and your teeth should never be clinched. If you're sprinting your cheeks should actually bounce. When running your hands should not be clamped into fist. Pretend you're holding a potato chip that you're not allowed to break. Once you've relieved the tension you'll see a huge jump in your capabilities.