Here is my un-scientific thinking on this. Don't think I know what I am talking about because I am not an expert.
Consider some illness that has a natural R value of, say, six. That means that if I get it and no one is vaccinated or immune, I give it to six more people. And they each give it to six more, and so on. Exponential growth.
Now, let's say that 50% of the population can't get this thing. They are vaccinated or they've had it before. So of my six randomly selected victims, it bounces off of three who are immune, but still gets three morons, uh, unvaccinated, folks sick. The R value is now three. Three morons. (and some unfortunate folks that can't get the vax).
The illness will spread exponentially until the R value goes below one. R value of 1.01 -- you are screwed. R value of 0.99 -- it will not spread. So, if the delta variant has a natural R value around 6, then we need more than 5 out of 6 people vaccinated or exposed to get that R value below one. Even if a super-delta variant shows up with an R of 10, we are good if more than 9 out of 10 people are immune.
Immunity may wane over time, so boosters may be needed to keep the immune population high enough to keep each variant's R value below one.