What is the practical significance of speed RPM in a propeller aircraft for a pilot? I am not able to correlate it with RPM in jet engines?
in propeller aircraft, the practical significance of propeller RPM is it is one component of the equation that determines propulsive power, the other being shaft torque.
If the propeller has a fixed (nonadjustable) pitch, then the RPM of the propeller is a simple indication of the power output of the engine, and the pilot manages engine power by adjusting tachometer RPM with the throttle.
Controlling the power output of a turbine engine is a more complicated process, and depending on the type of engine and its application, the pilot may use pressure measurements in the different stages of the engine or ratios of those pressures or shaft RPM's expressed as percentages of full power to manage the power output of the engine.
RPM in a propeller aircraft is typically under 2400, as the prop spins at the engine RPM speed. Above 2700 the tips of the propeller begin going supersonic and make more noise than anything.
Jets engine spin much faster, as discussed here Which are typical rpm values for aeronautical turbines?
There are three primary cases for use of RPM in aircraft that differ by engine type: piston, turboprop and turbofan. In all three cases RPM refers mainly to two speeds, propulsor and engine. They may be indicated in percent of maximum (usual for turbine) rather than as a specific speed (usual for piston).
Piston engine- the propulsor is the prop and the engine speed measured is the crankshaft. Usually there is no gearing and both are the same, so there will only be one gauge in an aircraft. Notable exceptions are warbirds with high power and correspondingly large props.
Turboprop - the propulsor is again the prop and the engine speed being measured is the turbine output shaft, fixed to the low pressure compressor. This is input to a gearbox since turbine speeds are too high to be useful in directly driving a prop. There can be two speed gauges in the aircraft.
Turbofan - the propulsor is now the front fan and the engine speed being measured is usually the core, the high pressure compressor. The front fan historically runs on the low pressure compressor shaft. PW inserts a gearbox between the front fan and the output shaft, making the drivetrain resemble the turboprop configuration. More complex engines may have three shafts, all running at different speeds.