Oscillator circuit with TL071 opAmp for amateur very short range AM radio
the video shows how to build an AM transmitter circuit using an opamp,
  some resistors and a capacitor.


It's a relaxation oscillator and here's a simplified version using a schmitt trigger: -



However, as a carrier wave it's poor because it's basically a square wave and not a sinewave. If you are going to transmit (illegally or not) don't use a square wave as an oscillator because you'll broadcast your transmission at the fundamental frequency of the carrier (say) 1 MHz and every odd harmonic up into hundreds of MHz i.e. you become a polluter.

Anyway, back to your question, When the inverter output changes state from zero to one, it charges the capacitor up (via the resistor) until the cap voltage triggers the upper limit in the schmitt trigger. This forces the output to zero and the capacitor discharges via the resistor. Back to square one and the process repeats.

If you can follow the above circuit operation then you should be able to figure out that your circuit is identical in nature. 

Hint: inside my circuit hides R1, R2 and R4 and, because they are hidden internally, there is no need to show the non-inverting input.