It refers to a system where a photosensor (usually a photodiode) is used to measure the light emitted by the light source. The system can then adjust the exposure to compensate for fluctuations in the light source; e.g. if the bulb dims for some reason, the exposure can be extended slightly to compensate for this.
The advantage is that you should be able to make very consistent exposures this way; e.g. when going from 0.3 to 0.6 seconds, you will get precisely one stop more exposure, instead of a little more still because of the bulb warm-up time. By definition, it can compensate for things like bulb warm-up time, bulb aging (depending on how the system is designed) and power supply fluctuations.
The disadvantage is greatly added system complexity. For virtually all darkroom printing, it's more of a gimmick than a necessity. Frankly, in my opinion, it's a solution in search of its problem. While it was useful in technical applications where extreme control over exposure is necessary, other approaches have superseded this for the most part (more consistent LED lighting being an obvious one) if the applications still exist anymore in the first place. In artistic printing, the net benefit is near zero since fine arts printers (which includes, by extension, the majority of amateur darkroom enthusiasts) adjust their prints using test strips and visual evaluation.
An argument could be set up that a closed-loop system is beneficial if you want to change e.g. enlargement (going from a small test print to a larger one), which will involve a change in exposure, and the closed-loop control will compensate for any non-linearities that accompany such a change. How practical this is, depends on your own perception and preferences. I've done quite a bit of work building my own enlarger light sources and in all honesty, I've never seriously considered including a closed-loop control along the Pictochrome-lines because I just didn't see the point of having it.