Yeah. I think it's only a Turboprop thing. I'm not sure if any piston engines have beta/reverse.
Here's my understanding from sims/flying with my dad/youtube. I'll be getting my complicated rating as soon as I'm done with my private pilot license, and I'll learn about it properly.
So at idle, with the prop lever forward, the pitch of the propeller is "fine", let's say at 1000 RPM. As you bring up the throttle, the RPM increases to the redline (let's say 2700 RPM), but it can reach it at less than full power. So then the governor sets in, and the pitch starts to increase to keep the engine/prop from overspeeding. After take-off, or at the end of climb, depending on the plane, I think, you bring thee RPM/Prop lever back to decrease RPM to a cruise climb or cruise setting, somewhere between 2200 and 2500 RPM probably on a lot of engines. This increases the pitch even more, without adjusting power. You'd bring power back too, but the RPM wouldn't change from doing that (unless you brought it back far enough to not be able to stay on the governor) the pitch would then just decrease a bit. You can usually find online speed vs. range tables for RPM/Power settings.
You can kinda think about it like going up in a hill in your car. For a given throttle position, the steepness of the hill is going to determine the car engine's RPM.
Turbo props are pretty much the same, except the prop spins much slower I think. I think they typically redline in the teens. And you manage power using torque, because the prop is made to take such a large "bite" of the air, I think you can over torque the shaft. And going into Beta is basically any position past the idle position, through completely vertical, when the prop makes no thrust, through to reverse. Beta is often used in taxi, because idle would cause too fast a taxi. It's kinda like throwing the clutch in to tool around a parking lot as speeds that would stall the engine of your car.
Here's a pretty good explainer of turboprop reverse thrust. http://www.12charlie.com/Chapter_14/Chap14Page007.htm
Newer planes had mechanical or computer controlled RPM, where there is just a single power lever, and the RPM is completely controlled by pre-set settings or computers. The Cirrus has the mechanical version, and the Diamonds, and some others go even further with full FADEC control to control the mixture as well, all through computers, so there's just the one lever.