To try and better explain it, lets begin with no feedback resistor, a tiny input signal slams and saturates against either rail, resulting in more like a square wave, this is because a small signal NPN likely has a current gain between 70-300 (Its "beta") this is clearly not ideal,
At stead state as the output will be resting somewhere close to center of the supply rails, and the input will be resting somewhere above where the tranistor begins conducting by the biasing resistors, placing it somewhere around lets say 0.5V on the base pin, and by adjusting this bias and adjusting how much its turned on, you can adjust where the output rests, generally centered between the 2 supply rails
The biasing resistors are feeding a tiny amount of current into the base of the transistor to turn it on, and as the output is at a higher voltage than the input, the feedback resistor is also summed into this, adding a very tiny amount of current, but at steady state you have already corrected this out.
When you have a signal coming in, you actually have a divider between the signal impedance, and the feedback resistor, the lower the value of that feedback resistor, the more influence it has over the input signal, as its inverted to the input signal this reduces the input amplitude, and reduces the effective gain of the amplifier.
Note this is more or less happening all at once, with some feedback the corrections ideally converge, but if you do something to add significantly more phase offset between the output of the amplifier (180 degrees) and its input, say bring it closer to 360 degrees, you can end up with an oscillator, where your feedback action applies in the wrong direction. this plays in to control loop stability and bode plots, handy tools, but depends on how far you want to dive down the rabbit hole for a transistor amplifier (you want a gain of less than 1 before non ideals add up to more than 180 degrees of additional phase shift, but for such a circuit, its likely in the MHz, not Khz)