KH is hardness of the water.
This is a fairly incomplete definition, because there are many different kinds of hardnesses defined for water. In particular to fishkeeping, the ones seen most often are GH (general hardness) and KH (carbonate hardness, the K comes from the German word for carbonate).
In very short, GH is a measure of all the hardness causing minerals in the water, the calcium, the magnesium, etc.
KH is a measure of the equivalent of the minerals in the water to a certain amount of carbonate. This is important because a given amount of carbonate takes a certain amount of acid to neutralize it. What this means is that the KH is a measure of how well water will keep a constant pH (this is also known as alkalinity and acidity, and it is proper to say that "KH measures the water's alkalinity" for example). That's why this is important when trying to tinker with your pH as a fishkeeper. A KH of 1 to 3 degrees is pretty low, and that means that the pH can be changed pretty easily. The acidic end products of the cycling process will probably even be enough to start changing the pH if the KH is not replenished often via waterchanges. A KH of 10 to 12 or more, on the other hand, is pretty high, and it will take a fair amount of stuff to change the pH of that water.
Finally, GH and KH are often correlated -- a high GH usually indicates a high KH -- but not always so. There are some waters out there with high KH and low GH, and vice versa, so to be completely sure of what your water is doing, you need to have both tests.
