It stands for "electrical conductivity" and it is used to measure how many salts are in water. It is also often referred to as "PPMs" which stands for "parts per million."
The higher the EC is, the more salts/nutrients are in the water. So, as a soil grower, you would generally test the run off from your pots to gauge where your nutrient levels are. I personally use PPMs myself so I might easily confuse ECs, and therefore will resist making any recommendations on proper ECs.
I am a hydro grower as well, so measuring and monitoring EC/PPMs in soil is better left to someone with more experience in a soil medium.
Regarding flushing - you are generally trying to REDUCE the EC, so you can flush either using plain water - typically running three times the size of the pot through it - or you can try to be more thorough and use a flushing agent, such as Florakleen, which is supposed to dissolve salts. For soil, a lot of people just water with plain water and stop all nutrient feedings two weeks prior to harvest.
I hope this answers your question and doesn't confuse you. 😀
Water is life.
Yep, @bogleg pretty well nailed it there. The more nutrient salts in your water the more easily the water is able to conduct electricity. That's what your EC meter is measuring.
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