Sziklai pair feedback loop
¨Q3 pushes current through R2 about the current gain of Q3 times the base current of Q3.

The base current of Q3 is the collector current of Q6, which is about the current gain times the base current of Q6.

The base current of Q6 depends on the voltage difference between the base of Q6 and the emitter of Q6. 

The voltage at the emitter of Q6 depends on how much current Q3 pushes through R2. This is how the collector current of Q3 affects itself through two transistors, the feedback loop. At low frequencies the feedback is negative, the voltage at the collector of Q3 will follow what's inputted to the base of Q6. 

The application idea of this circuit is to make a boosted emitter follower (search for emitter follower, it's one of the most basic transistor applications). A single transistor emitter follower is enhanced by adding the other transistor, in your case the extra component is Q3.  The result is like a single transistor emitter follower which contains a very high current gain transistor, the effective current gain can be thousands or tens of thousands. 

Unfortunately the non-ideality of the transistors make the circuit behaviour complex. An example:





The output voltage at NODE2 should follow the input voltage with about 0,6V difference. The input voltage (blue) drops from +6V to +4V as a -2V step. One could expect that the output voltage (yellow) should drop as much but with a ramp due the slowness of the transistors. Instead of it one can see a short peak upwards before the expected drop. 

I have seen the same with oscilloscope, too. I must admit that applying fast pulses was a whim with no original intention to amplify fast pulses with multistage feedback amplifiers, so this example is theoretical only.

High frequency oscillations occur if the transistors can handle so high frequencies that the wiring (inductance, capacitances) and junction capacitances inside transistors together cause so much phase lag that the feedback starts to be positive. That can happen easily if there's long non-matched signal cables or the circuit is built on a breadboard.

An example:



The curve is the voltage over the resistor. The circuit oscillates at the resonant frequency of the LC circuit. There's no intentional RF resonant feedback circuit, only something which is possible with long input signal wires. The oscillation amplitude doesn't build up to full supply voltage wide swinging because the loss in the NPN transistor BE junction is an effective amplitude limiter for the resonant circuit.

ADD due the comments(which started to turn to attempts to find errors and partially deleted for that reason)

Darlington emitter follower is also a 2 stage feedback amp. The feedback route there isn't obvious like in Sziklai pair where a wire exists from the load to the emitter of the NPN transistor. The emitter can be seen as the 2nd input of the 1st amplifying stage.

In emitter follower the output terminal is the same as the 2nd input of the transistor, no wire is needed, but the effect is = feedback as others try to show with equations. The input current depends on output voltage. Darlington pair emitter follower has 2 emitter followers cascaded. The output voltage affects also to the input current of the 1st transistor because that depends on the voltage at the base of the 2nd transistor which is the sum of the output voltage and voltage drop in the BE junction of the 2nd transistor.

With reactive input circuit a darlington pair emitter follower oscillates like the Sziklai pair: