Strip away all the specific programs, rep schemes, and training philosophies, and almost every one of them is built on the same underlying idea: progressive overload. Your body only has a reason to adapt — build muscle, get stronger, improve endurance — when it's asked to do something harder than it's already handling. Without a gradually increasing demand, it has no signal to change.
Overload doesn't just mean adding weight to the bar, though that's the most obvious lever. You can also increase the number of reps at a given weight, add an extra set, shorten your rest periods, slow the tempo of a lift, or simply improve your technique so more of the effective muscle is doing the work. Any of these raises the total demand on the muscle relative to last time.
The research on training adaptation (going back to Hans Selye's General Adaptation Syndrome model in the 1950s, and refined heavily since) describes this as a stress-recovery-adaptation cycle: a training stimulus is a stressor, recovery is where the adaptation actually happens, and the next session needs to apply a slightly larger stressor than the body has already adapted to, or progress stalls.
This is also why "more is better" is a myth. Overload has to be progressive, not maximal — jumping the weight up too fast outpaces what connective tissue and recovery capacity can handle, which is a fast route to injury or burnout rather than faster gains. Small, consistent increases beat occasional large jumps.