The Surgeons loop is a quick and easy way to tie a loop in a line or leader. I am not sure exactly how strong it is, but for the purpose that I use it, it is definitely strong enough and has never failed.
I use the Double Surgeon's loop for my loop in my tarpon fly leaders. I will do a double nail knot loop in the end of my fly line and then attach my butt section to the fly line with a loop to loop handshake connection. Many people ask why I prefer this loop to the Perfection Loop (Click here to see video of Perfection Loop)
I much prefer the Surgeons loop over the Perfection loop at the end of a fly leader for tarpon because the tag end of a Perfection loop sticks out at a right angle to the line. When fishing for a large tarpon, we will use a leader of 12-15 feet and it is required to bring the leader all the way inside the reel to land them. The loop will travel in and out of the rod guides many times before the final landing. The Surgeon's loop is far smoother through the guides due to it's tag end laying parallel to the line rather than perpendicular.
There are probably countless other applications for the Surgeons Loop, but for my purposes, it is simply used for a loop to loop from Fly line to leader.
Here is how to tie the Surgeons Loop. If the video does not display for you, please click here
All the best,