A strop is a piece of leather used to polish an edge. They were used all the time in the days of straight razors. In other words, they are the final step in making an edge "razor sharp" and are used by pulling the edge along the leather rather than pushing it. Straight razors needed a polished finish on the blade for purposes of comfort in use.
What folks should understand is that most knives don't benefit from being "razor sharp." Actually they work better if they don't have a polished edge and have some coarseness to the edge. It is the geometry of the edge that determines performance, not the final finish for most applications.
I learned to sharpen when I was a fine bookbinder many years ago. The tools had to be very, very sharp indeed so sharpening was a constant effort throughout the bookbinding process. We used to hollow grind large chisels at very acute angles and then sharpen them to a polished finish. We would use them like a knife in a fixture to trim the tops from folios to make them smooth and even as you see them in almost any book. These chisels couldn't be used for anything else because the edge geometry and edge finish were appropriate only for trimming folios. The same holds true for a leather paring knife. It does a great job paring the suede side of leather but doesn't do anything else very well.
I sharpen kitchen knives to what I would describe as a coarse finish and sporting knives to a medium finish (about like a factory edge.) I don't use stones any finer than medium for sharpening general purpose knives and they perform best that way. If I need to demonstrate sharpness by peeling unsupported newspaper into strips, I can polish the edge temporarily but then I roughen it when I'm done because I spend little practical time actually peeling newsprint.
And to the original poster. I have about 1/2 dozen strops like the one you made (with the wood and leather flush at the edges) that I used for bookbinding. I usually had the suede side of the cowhide on one side and 400 grit carbide wet/dry sandpaper on the other side. I could touch up the edge with the sandpaper and then flip the strop to polish the edge on the leather. Most bookbinders use a similar sharpening device and keep it on the bench all the time since it's used every few minutes. I still use them occasionally today even though I have gone to powered sharpening for the most part. Take care.
