Its simple, really. We start with the premise that the more we lift heavy, the bigger and stronger we get. Plus, when you engage in heavy strength training, you do two things: 1) stimulate anatomical and physiological adaptation, and 2) deplete nutrients from muscle cells and neurons. Both things impact each other: the more adaptations the body needs to make (be they anatomical or hormonal), the more nutrients are needed. If your body is lacking nutrients, it is lacking the means to lift heavy.
A person who lacks any supplements, as I have often experienced, must be fully aware that maximum gains are not possible. You can get big and strong, but not to your genetic potential. The issue is recovery. Solid foods take time to digest, and therefore the nutrients aren't readily available for your muscles to use to recover. This means your muscles need more time to fully recover before you engage in heavy lifting again. Instead of benching three times a week with great intensity, you'd probably have one heavy/intense day and one light/moderate day.
When you have supps, be they simple, like whey protein, or advanced, like PLAZMA, the game is changed because your recovery time is shortened. Shortened recovery time allows more work to be done. Instead of one heavy/intense bench session as above, you could probably fit two (possibly three) in. The more you can lift heavy, the bigger and stronger you can get.
If you are on no supps, and doing an extremely high-intensity plan, like Meadows Reactive Pump, or CT's layer system, you'd conceivably have to make some concessions or adaptations to the program to provide for the increased recovery time. Such concessions minimize the effectiveness of the program.