It is very important to monitor your heart rate during exercise. The faster your heart beats per minute, the harder your body is working and consequently the more calories you're expending. This can be used as an objective measurement of exercise intensity. In addition, individuals with chronic disease (e.g. hypertension, coronary heart disease) should monitor their heart rate to ensure they do not over exert themselves during exercise. For these individuals staying within their target heart rate is very important.
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National Academy of Sports Medicine answered
If you have health problems related to heart disease or being very overweight, measuring heart rate can be a prescription number to make sure you don’t overdo it and it also can act as gauge of progression. Endurance athletes also use heart rate to tell them what pace to run so they can delay fatigue by conserving carbohydrate stores. If weight loss is your primary goal, you don’t' need to know heart rate unless it helps you push yourself harder by seeing the number. For weight/fat loss, with all factors being equal (calorie intake, daily activities, etc.), it's simply the harder you work the more calories you will burn, which will lead to more absolute body fat loss.