The irony is that for high intensity intervals to work,
there has to be solid rest in between sets,
so that each set can actually be high in terms of intensity.
In other words, if you're slopping through each round because you're so tired from not enough rest in between, then none of them in particular will draw out of you the kind of effort which warrants adaptation.
So "high Intensity"? Think of a soccer athlete sprinting for a loose ball thirty yards away.
If you search queries in the "pubmed" database, there is a difference between Sprint Interval Training (SIT) and High Intensity Interval Training (HIIT). What I am speaking to in this post is, ironically, not the HIIT modality but the SIT mentality (Sprint Interval Training being the one where individuals are performing an action for a shorter duration yet closer to or at 100% of perceived exertion).