Conductivity used in the sense of water parameters is a measure of the total dissolved solids in the water. This is because when most solids dissolve in the water, they actually are solids that dissociate into ions in the water, in the form of PN dissolves into P+ and N-. (P for positive and N for negative.) For example, salt, sodium chloride, NaCl dissociates into Na+ and Cl-. Calcium chloride, CaCl2, dissociates into Ca(2+) and 2Cl-.
And, the more ions in the water, the easier is it for electrons to flow. This is because there always has to be a charge balance in the water, when an electron is added to the water a negative ion has to be consumed so that the charge remains neutral. And, when that electron leaves, a negative ion has to reenter the water. The more ions in the water to begin with, the easier it is to find one to be consumed, and so the electricity flows easier.
Conductivity is the inverse of resistance, and actually one of the units conductivity is measured in is the mho (which is Ohm backwards, the Ohm being the common unit of resistance), though usually the unit of conductivity is the siemen (S).
You can buy conductivity meters, and the price is going to vary a lot, depending greatly on the accuracy you seek. I am pretty sure you can find some pretty cheap, inaccurate ones, and you can find very expensive accurate ones.
How it affects fishkeeping is that is it a measure of the total solids in the water, also known as TDS. GH gives a fair amount of similar information, though not exactly the same. GH only measures the hardness solids, though generally hardness solids is all that is going to be in the water in any significant concentration. So, in any way that hardness affects the fish, the TDS or conductivity affects the fish in the same way. Just a different way of expressing it.
