It's in that article.
Freshwater
When starting a new fresh water aquarium and before introducing fish, it is good practice to measure the water hardness value (GH) and evaluate if this value is suitable for the fish you are about to introduce. In other words, by knowing the GH value of our aquarium water, you can determine which species of fish will thrive in that type of water.
In a newly established aquarium, conductivity will be roughly related to General Hardness (GH= sum of divalent ions, mainly Calcium and Magnesium) and TDS (Total Dissolved Solids) values: µS/cm x 0.5 = ppm TDS x 0.056 = dGH.
Therefore, when buying a freshwater fish, it is very important to know the EC value the fish was living in, and which level will be needed to keep the fish healthy.
For community freshwater tanks, the EC value may generally range from 100 to 300 µS/cm; Discus, Paracheirodon and other soft-water species require values below 100, while Cichlids from African lakes (Malawi e Tanganyika) thrive at values above 500 µS/cm.
Basically it's an indicator. The EC itself isn't what you are worried about but rather what's causing it. The graph on the page shows a rise in EC which was a signal to the aquarist something changed in the tank. They tested and found nitrates had elevated. In a marine tank EC is a good indicator of salinity.
EC is something I've never worried about measuring but I can see that it could save someone time. For example if I perform several tests on my tank this takes time and money for tests but if I measure EC then I really only need to run those tests when my EC has changed. That's really the value I see in it.
High EC does not mean your fish are getting electrocuted but can mean there is something about the water that is impure. Pure water, like distilled water, has little conductivity but when we add stuff, nitrates, TDS, etc. the EC goes up. When we know our baseline EC we can determine changes in water quality by the rise in EC.
That's pretty much it. Not something I worry about myself.