Intensity to me if volitional effort regarding the anaerobic energy system.
For example, pushing to muscular failure is higher intensity than stopping one or two reps short. Doing endurance activity, though, an extra mile is not necessarily a "higher" intensity effort because the relative effort to begin with is low. The first mile will be accomplished faster and would be higher in intensity and more productive than the second mile. The results of running an extra mile past what you previously accomplished will do little more than add an extra 150,000 tons of impact force to your knees, hips, ankles, and so forth. Defining this specifically can get pretty complicated so common sense should be used.
For example, pushing to muscular failure is higher intensity than stopping one or two reps short. Doing endurance activity, though, an extra mile is not necessarily a "higher" intensity effort because the relative effort to begin with is low. The first mile will be accomplished faster and would be higher in intensity and more productive than the second mile. The results of running an extra mile past what you previously accomplished will do little more than add an extra 150,000 tons of impact force to your knees, hips, ankles, and so forth. Defining this specifically can get pretty complicated so common sense should be used.