The largest misconception in the fitness world over the past 10 years has been what “intensity” means.
The term has been thrown around in acronyms like HIIT (High Intensity Interval Training) and in the definition of CrossFit (Constantly varied functional movement performed at High Intensity). In both of these worlds the word intensity came to mean working out at full throttle energy levels. Essentially go as hard and as fast as you can until you drop.
We need another understanding of intensity if you are actually going to reach your athletic and fitness goals. (I would argue this was the original meaning in CrossFit as well, until competitions began.) This new understanding is simply that intensity is all about having high intent. Whatever you are working on in your training does need to be done with high intensity. But this can include stretching or tempo work, not just circuits and fitness races. You will get the most out of any workout if you approach it with strong intent on doing it correctly.
Interestingly enough when you go into the gym and workout as fast as possible you usually completely miss the intent. You also likely did multiple exercises incorrectly, missed the benefits, and risked injury. Flying through a set of squats does not result in the growth possible from focusing on each rep and performing them correctly. During your workouts set your intent ahead of time and then focus on the true desired outcome for the day.