What makes the coming comet increase/decrease in brightness? I understand C/1979 Atlas Y4 is potentially going to rapidly increase in brightness and visibility to the point we can see it very well in May-ish, in the Northern hemisphere.

I am wondering why it's not predictable whether or not it will, or what processes affect the brightness.  If it's simply reflection, why would it dim or brighten? I really don't think I understand comets.
The nucleus of the comet is small and dark. We never see comet nuclei with the naked eye. The visible part of a comet is the coma and sometimes the tail which are made of dust and gas that have vaporised off the comet's nucleus by the heat of the sun.  

Now comets are unpredictable.  They get more active, producing more dust as they get nearer the sun, because it gets hotter.  But sometimes there might be a sudden jet (as part of the surface of the comet gives way) and releases lots gas and dust.  Or the comet may develop a "crust" that prevents much dust from escaping. These events can cause a comet to become much brighter or remain dimmer than expected.

Comets are active and dynamic bodies. And so they are intrinsically hard to forecast.  Extreme examples of this are 17P Holmes, which went from magnitude 17 to magnitude 2.8 in two days, probably due to a crust layer cracking.