Why is monitoring heart rate a common technique to determine exercise intensity?

The harder and more intensive your exercise is, there needs to be a proportional amount of oxygen-rich blood circulating to supply your body with the needed oxygen to continue.

Explanation:

As you exercise, you start to use more oxygen because your body is doing more work. As you use your muscles, there is an acid called lactic acid that starts to form on your muscles that causes the burning sensation you feel. The harder your exercise , the more of lactic acid there will be. The oxygen helps to clear out this lactic acid, while still supplying your body with the oxygen it requires to all body parts so they can function properly.