Why does this two NOT circuit oscillate?
This circuit is a variant of so-called "astable multivibrator", see Wikipedia.


  An astable multivibrator consists of two amplifying stages connected
  in a positive feedback loop by two capacitive-resistive coupling
  networks.The amplifying elements may be
  junction or field-effect transistors, vacuum tubes, operational
  amplifiers, or other types of amplifier.


Two inverters form a non-inverting amplifier, so the feedback loop is positive. Timing for flip-flops is determined by capacitors values times some input impedance (or current, for TTL). 

CLARIFICATION: The TTL inverters have essentially DC floating inputs in this circuit. Initially, parasitic leakages move the input voltages up crossing the switching threshold area, so the gates essentially enter the linear amplifier regime. The rest happens similar to the ordinary BJT multivibrator, initial state is based on realistic differences in element parameters, and then the switch frequency is determined by discharges of caps into input impedance of the circuit.