The RHZ is only found in boost and flyback converters operating in CONTINUOUS CURRENT MODE.
I think the easiest explanation of the phenomenon is that given by Pressmann.
In a boost (or flyback, which is a boost-derived topology) operating in continuous current mode, the duty cycle SHOULD NOT CHANGE WITH THE LOAD. That is because the duty-cycle is only a function of the input and output voltages. For example, for a boost operating in continuous current mode, the duty-cycle is:
DC=1-Vin/Vo.
Obviously this does not depend on anything else other than the input and output voltages. (In practice, a small change is observed, since there are load-dependent voltage drops in the transistor, inductor and diode, which effectively get subtracted from thos voltages).
We have established that the duty-cycle should not depend on the load. But a sudden increase in the load current will cause the output voltage to decrease slightly, for the reasons shown above: the voltage drops in the transistor, inductor, diode will all increase with increased current.
This output voltage drop will cause the error amplifier+PWM to take some action and bring the output voltage back to the initial value, although the change may be only small.
But what does the error amp/ PWM combination do in order to increase the output voltage? It will INCREASE the duty-cycle. But this results in NARROWING the current trapezoid during the flyback (reset) portion. But this is WRONG!!!!
This results in a temporary DECREASE in the output voltage.
The situation does not last forever, though. The increased duty-cycle causes an increase in the transistor on time and so the transistor current (and inductor energy) will have more time to increase. Thus, eventually the current will establish itself at the correct level, the output voltage will increase and the error amp will decrease the duty-cycle to the correct value.
Without going into details, as you can imagine this process of the current increasing to the new value takes time and this depends on the inductance, therefore the RHZ depends on the inductance.
So an increase in the duty-cycle results initially in a DECREASE of the output voltage! Exactly the opposite of what is necessary!
This is the RHZ effect: the error amplifier tries to compensate but the effect is "THE WRONG WAY". (In a Bode plot a RHZ affects the gain like left half-plane zero, but it affects the phase the opposite way, like a pole; since the phase is reversed, you can say it goes the "wrong way").
The normal solution to the RHZ issue is to decrease the bandwidth of the error amp. You can understand why by looking at the Bode plot (remember, the RHZ bends the gain curve up by 20dB/dec, but lowers the phase margin just like a pole does).
Or, intuitively, you can see that you do not want the error amplifier to respond very quickly, since you know it will cause the output voltage to change the "wrong way", so you slow it down so that by the time it responds, the inductor current has already risen somewhat towards the new value, so the effect of the RHZ won't be so noticeable.