Governor mode can be really nifty, as it will keep your head speed constant even in a rapid, elevator-style descent (which would normally dramatically speed up your head speed). However, the price you pay for the convenience of a consistent head speed is a loss of power, as the governor sacrifices top-end power for consistent speed under varying loads.
My governor-ed throttle curves are flat 77% and flat 85% on my T-Rex. A full-pitch (10 degree) climbout in governor mode at 77% sees no loss of head speed at all, while at 85% head speed drops about a hundred RPM on the way up. If the power seems lacking in governor mode, just go up one pinion size (11 tooth to 12 tooth, for instance) or try bumping your timing mode and throttle response from Low to High.
Align fixed a lot of things with governor mode on their more recent ESCs. It's not an amazing change, but flying in governor mode feels more consistent and also draws fewer amps over the course of the flight than my curves.
If you have good throttle and pitch curves, you won't notice much of a difference with the governor. If they were way off, you will notice a pretty enormous change in head speed variation.
Actually that (rather old!) explanation was not 100% accurate.
Governor mode wont prevent the rotors from overspeeding in a rapid descent with negative pitch applied. In that case the rotor 'windmills', and due to the one way bearing it can spin faster than the motor is turning, so governing the motor can not control headspeed under that circumstance.
What governor does do is control headspeed during normal flight (i.e. when the rotor is driven by the motor). The governor monitors RPM and if it detects a drop it automatically increases power to compensate. Vice versa if it detects an increase in RPM it reduced power.
It works very much like cruise control in a car where engine power is adjusted to maintain the speed you set, even when the car goes up or down a hill.
The part about sacrificing 'top end power' is also not really correct. If you have your governor set high enough then the motor will still reach it's maximum possible power, so you don't 'sacrifice' any power as such. The fact that you have (say) 80% set on the governor does not mean that power is limited to 80%. Governor % is not the same as throttle %.