Why does this circuit oscillate?
It's a phase shift oscillator. 

Normally, feedback from the collector to the base acts "negatively" and this is quite important for some amplifiers. This is because the collector signal is the inverse of the base signal (also known as 180º out of phase). Anything fed back does so without causing oscillations. This type of feedback is also used in op-amps for controlling gain.

On the circuit in the question there are a bunch of components that take the collector signal and phase shift it enough so that at a particular frequency, it appears in phase with the base signal and reinforces it. This makes it oscillate.

On a more technical level, the feedback formed around R2, R3, R4, C1, C2 and C3 act as a "mild" notch filter. It should be said that the intent of a "good" notch filter is to totally remove one frequency (such as 50Hz or 60Hz when mains AC is a problem). The frequency which is notched out will be phase shifted by 180º and if it isn't totally notched-out (as in a good notch filter) what remains will feed back and reinforce the original base signal causing it to oscillate. 

It doesn't matter that the signal might be attenuated by 20dB, there will still be enough signal left to be amplified and generate a sinewave.