I'm one of those people that like to know exactly why I am doing something that takes up my time, so basically my question is what is the water change exactly doing to the water? What is it adding/taking away to/from the tank? What is it doing to the PH, alklinity, calcium?

the water change is dilution. corals produce noxious compounds as well as your fish. the longer you dont change your water the lower the ph + more toxic compounds.= slow coral growth or even death .may not be right away but give it time . your corals take in calcium alkalinity + much more outside or the basic test kits. water changes provide your trace elements {read the back of your salt} you will probably need to add some calcium/alkalinity on top of water changes . in my opinion frequent water changes are one of the most important things you can do as long as you do them right. ihope this helps if not post it