This knot is one of the many improvements Lefty Kreh has made to the sport of fly fishing. It is much stronger than the clinch or improved clinch but more important, allows the fly to move more freely than with a clinch-type knot, especially if you're using heavy monofilament line (nylon or fluorocarbon).
The downside of the knot is that it's visually bulky and/or distracting to the overall shape of the fly—only a concern if you're using smaller flies and the fish can see the fly in profile. I don't recommend it for dry flies. But if the fish are likely to be chasing the fly, or you're using large flies where the knot size is relatively unimportant, it's the perfect knot to preserve the life and movement of the fly.
It's a must in saltwater fishing for tropical flats species like permit and tarpon, and for bluewater fishing for cobia, mahi mahi, and various other species. I recently used it for tuna fishing with Journey South Outfitters in Venice Louisiana. The connection to the fly was with 60-pound fluorocarbon, so a three-turn no-slip knot was easy to tighten (with pliers of course) and gave the fly plenty of movement. The standard no-slip knot (as shown here) is with five turns around the standing line, but that's for 20-pound-test line or lighter. Use lip balm on the line to help tighten the knot without abrading, and don't make the mistake of trimming the tag end too short. Leave a little tag to be safe.