Flushing with Reverse Osmosis or Distilled water (of course any water will do, but RO is 0 ppm) will stop adding nutes tot he soil/hydro, allowing the plant to feed on everything, and once depleted, starts feeding on itself for nutes/sugars/chlorophyll. The chemical concentration in the plant decreases as the plant starts autuming off and eating at it's leaves. Salt buildup within the soil/plant decreases. All of this in the end will help create a great tasting smoke that is less harsh. Yes, proper drying & curing will make a huge difference, too, but proper flushing AND proper drying, curing makes the absolute best bud. If you're a conneissuer, you should easily be able to see the increase in quality. Esp if you have flushed & non-flushed side-by-side to quality test.
If you are in soil and doing pots, remember to flush and strain some of the runoff at the bottom into a cup and test the PPM of it. You will see it go down the more you flush and the more the plant eats, until you are getting clear runoff and pretty much just getting a ppm of what the water is before it goes into the soil. After you get the PPM to that level, assume you need atleast another 3-5 days flushing for the plant to start eating at it's own leaves for nutrients/sugars.
If you are in hydro, you want to swap your reservoir out with RO/Distilled, or the best quality filtered water you can get your hands on. This will start to immed pull nutes & salts that are builtup throughout the system and in/on the roots. As it flushes, this will raise the overall PPM of the water throughout as it starts to break down other stuff. Be sure to swap your reservoir out daily, or every other day at the very least. Using Final Flush solutions can help, as chelating agents will bond with salts and other bad things you don't want in your plants before you smoke.
If you are in the ground like me, you can still flush, it just takes longer and won't flush completely. That's why I go organic. Makes a huge difference. No overloaded, synthetic chemical taste/flavor.
Properly flushing AND properly drying/curing your buds with patience is the absolute best way to achieve conneissuer level buds
Hope this helps! +rep if you like! =)
Cheers!