An RC phase shift oscillator is a sine wave generator. It only needs a DC power source. No input is provided for circuit. What is happening inside the RC phase shift oscillator? How is a sine wave being generated there?
The amplifier, together with the RC networks provide greater than unity gain at some frequency, that's the frequency it oscillates at.
How does it start? All circuits have broadband noise. The noise is amplified, and the oscillation builds exponentially.
Eventually the oscillation amplitude is large enough to hit some limit. Either the amplifier hits the rails, so loses gain, or in a much tamer process the amplitude is detected and used to turn the gain down to unity. Either way, the oscillation stabilises at some level.
These oscillators usually do not start when simulated, as a simulator has no noise. Typically you would use initial conditions to give it a kick.
Such an oscillator can be seen as an amplifier that creates its own input signal.
Example: An amplifier with a gain of A=10 and an output amplitude of 10 volts needs an input signal of 1 volt (in reality 1.1 volt or so to allow a safe start of oscillations.) Hence, the required input of 1 Volt is derived from the output signal using a feedback factor of k=0.1).
As a consequence, the loop gain Al=A*k=1 (in practice we require Al=1.1 or so). Because this condition must be true for one single frequency only, the feedback circuit must contain a frequency-selective network - in your case an RC-phase shift chain (highpass or lowpass) that provides the necessary damping at the desired frequency.,