As many people have mentioned in comments already - you are looking for a pyramid set, namely "increasing/decreasing rep range during different sets of one movement". It is not a hard definition, and people use that to apply to weights as well.
Dropsets is another similar strategy. In drop sets, you generally perform a heavy lift in a certain rep range (generally low), then quickly deload 10-20% of the weight, and perform a lift again. It continues until you are working with something super light.
The idea is probably nothing new and came from all over the world. Bodybuilders were definitely using pyramids and drop sets for ages. link
Pyramid training is often used to pass plateaus, when a trainee is unable to add more weight on traditional sets. It could add benefit to hypertrophy (size increase), because you stay longer under load, pump more blood into the muscle, etc.
Honestly, don't over stress about it. If you want to do those pyramid sets for fun - do them. But at the beginner level (and unless you participate in strength competitions - you are a beginner) you can progress with straight sets by simply adding more weight to your lifts, or more reps to your body weight movements. If you ever reach a point when you are unable to add more weight to your lifts, or add more reps to your body weight movements, assuming you are doing something really heavy, then pyramids or drop sets or other movement patters could be useful in your training.