Nutrition is something that must not be overlooked when exercising. Whether your goals are to lose fat, gain muscle, for performance purposes, or just living a healthy lifestyle, nutrition is something that one should take into account.
The most popular reason for exercise is obviously to be in shape - lose unwanted body fat. It goes without saying that when you're trying to lose unwanted body fat you must pay attention to what you consume and how much you consume. The golden rule is that you should consume less energy than you use for weight loss to occur. If you don't consume less energy than you use then there is no point in exercising (that is if your goal is to lose unwanted body fat). Also when you are on a calorie-restricted diet you need to eat nutrient-dense food. Yes, you will still lose weight if you're in a calorie deficit, but there will be several other problems that you will need to deal with like a hormonal imbalance that might force you to gain weight.
If you are training to gain muscle mass then without nutrition, again, this is unachievable. Without getting the right amount of protein, protein synthesis will not occur (muscle building). Without getting the right amount of carbohydrates then you will not be able to fuel your workouts and get the proper stimulus from exercises to build muscle.
For performance, nutrition is vital if you want to perform at your best ability. Performance on game day or even recovery from a game day or practice requires adequate and proper nutrition. Various micro and macronutrients are required for your body to function at its best.
And obviously, it goes without saying that you need to take nutrition into account if you want to be healthy in general. The stress caused by exercise needs to be nourished and refueled with a nutrient-dense diet, for if not then you are just causing stress to your body from which you will eventually break down.