An signal that is attenuated on purpose is one whose amplitude is reduced to the amount that is required.
Simply put, to make an oscillator without too much distortion, you need just enough positive feedback so that the overall gain is a little more than 1. Since the oscillator's amplifier has a certain amount of gain, you must attenuate its output by about the same amount so that the overall gain is a little more than 1. If you attenuate its output too much so that when it amplifies it then its output is less each time around, then it won't oscillate. If you don't attenuate the feedback enough, then the signal is amplified more each time around and its output will be square waves with lots of harmonics.