The basic idea why you should Strop a cutting edge, like a knife, is to remove the micro-burr that, unavoidably, remains after the re-sharpening process has been completed on a water stone. This micro-burr will make your knife edge appear sharper than it actually is, because it will have a very thin microscopic piece of wire, just a few molecules thick, which is very weak and easily detached from the cutting edge, leaving behind a somewhat duller edge than would be desired.
The ‘Stropping’ process, when a knife has been properly sharpened, actually transforms the newly sharpened, apparently sharp, cutting edge into a durable, razor sharp, cutting edge. The ‘Stropping’ process also polishing the cutting edge after the micro-burr has been removed, this also removes the microscopic furrows that are left behind by the grit particle of the water stone.
In a nutshell, the ‘Stropping’ process leaves the cutting edge sharper and stronger, which will make it last a whole lot longer than without stropping.
If you have a double-sided strop, such as the Double-Sided Hand Strop, you can treat one side with a good quality Honing Paste that will enable you to achieve a polished razor edge in a much faster time, than it would be possible without. With the addition of a high quality honing paste, the ‘Stropping’ process is dramatically accelerated, since a honing paste is very slightly abrasive. The treated side of your strop will therefore act as an incredibly fine hone that will bring back a slightly dulling cutting edge to a razor sharp cutting edge (assuming it was razor sharp to begin with). Treating a Strop in this manner actually changes it from a ‘Razor Strop’ to a ‘Honing Strop’, so It is important to not contaminate the clean side of a Strop with honing paste.
The application of honing paste (to one surface of your strop only, the other surface should remain untreated) helps to significantly extend the life of your knife’s cutting edge before it will require to be re-sharpened on a water stone again.