Some vitamins are fat soluble - Meaning, if you do not consume fat in your food, those vitamins cannot be absorbed by the body
Fat forms a layer between your skin and muscle. This acts as a water proof layer below your skin and also helps regulate body temperature and shield you from excess cold/heat outside
Fat is essentially reserves of energy. When you are fasting or during starving or during very strenuous physical activity, these fats would be converted to energy by the human body.