Conductance (or conductivity) is the ability of the water to conduct electricity, and it varies with the amount of chemicals dissolved in the water. For example, road salt drives the numbers way up. Or it could be nitrogen and/or phosphorous from agriculture runoff - a conductivity meter can measure the conductance, but it can't tell you _what_ is dissolved in the water. It's used as a flag for further investigation.
The clarity of the water is "turbidity" and it can be measured by a simple device called a secchi disk; you lower it into the water and measure how far you can lower it before you lose sight of it:
We have a handheld meter for conductance, but handheld meters for turbidity are crazy expensive, I don't know why.