An internal combustion engine is designed to produce power between two RPM limits, which is called a 'power band'. Generally, the more RPM, the more power the engine is producing. Sports cars and high-performance cars have tachometers so you can see the RPM and intentionally keep it between the limits. plus there is a 'red line', the highest RPM an engine can go before it might damage itself.

Some engines can be increased in power by doing things to raise their RPM limits, like overhead cams, lighter pistons and connecting rods (to reduce reciprocating weight), etc.

Automatic transmissions have sensors built in to read the speed of the engine and change gears automatically to keep it in the desired RPM range. They can also read how far the gas pedal is depressed, so they will shift later (higher RPM) if they see you are trying to accelerate fast. Also some auto transmissions have a switch to select a higher rev range for more power at the cost of less gas mileage, or more fuel economy at the cost of faster acceleration.

Engine RPM refers to the crankshaft. Now you know just as much as you did before. GO READ A BOOK!

It refers to the crankshaft. Every rotation of the crank is one revolution. When your car is running at 2300RPM's it means the crank is turning 2300 revolutions per minute.

Revolutions per minute of the *crankshaft.

so how come that the crankshaft can be at a same RPM but on different speeds?

That's because of gears in your transmission. Even an automatic shifts gears.

The crank shaft, or twice the cam shaft and distributor if it has one.