It is a measure of what is in the water besides H2O.
Most people do not realize that pure water is a poor conductor of electricity. What makes water a good conductor is all the particles/microorganisms in it. So what is measured in terms of conductivity, is how well the water conducts. The better it conducts, the more stuff is in it. A lot of it will also show up as TDS- (Total Disolved Solids). This is actually measured in the same way as conductivity, but then the meter converts it to TDS having compensated for the temp. A portion of conductivity and TDS is what we fishy folks know as Hardness (GH) and Alkalinity (KH). Ions also affect conductivity.
Basically, depending on one's need for a measurement, the GH/KH kits will be the least accurate and the conductivity readings the most accurate. The TDS reading will vary in their accuracy but will pretty much track conductivity. I use a TDS meter for help when simulating dry and rainy seasons for plecos.