I'm also a newbie struggling to understand the chemistry behind aquarium water parameters (for breeding purposes), so learning about pH, KH, and GH have been a priority. Because forum threads on the topic usually only confuse me, I hope no one minds if this beginner imparts a few of the basics he's picked up recently:
wkndracer is right, GH is unrelated to pH and KH.
pH, as you likely know, measures the acidity/alkalinity of water, or the ratio of free floating hydrogen ions (H+) to hydoxide ions (OH-), on a logarithmic scale between 1 and 14. I imagine you understand pH, but if not feel free to ask more.
KH, or carbonate hardness, is directly related to pH. It measures carbonate and bicarbonate ion concentrations, and reflects the buffering capacity of water. This is the water's ability to prevent fluctuations in pH. The higher the measure of KH (on whatever scale, I have found several), the more stable the pH. Extreme (or even minor) changes in pH can be detrimental to fish and plant health, so it is important to maintain water with some KH (RO/DI water, for example, has none).
GH, or general hardness, is what is usually referred to by the term "water hardness." It measures metal cations in the water, specifically calcium and magnesium. I do not know if it includes the concentration of other metals or only these. It does not affect pH or KH in any way, but rather is a completely separate parameter.
On a side note, GH is related to both TDS (total dissolved solids) and conductivity. TDS is a measure of, you guessed it, all the dissolved metals in the aquarium water, including some not counted in the GH measure. For this reason, TDS can often be used to give a good approximation, but never an exact measure, of GH. The attractions between the metal ions measured in GH and TDS is what affects the conductivity of water, and so these three parameters be used to approximate each other.
Different fish and plants, have different preferences for each and every one of these parameters. Usually they do best in water than closely mimics their natural environment, although many species can adapt to a wide range of conditions. For breeding purposes (and possibly for the propagation of certain tricky plants) the conditions may need to be replicated more exactly.