Try thinking on a microscopic level for a minute. If you look VERY closely your will see that the edge of your razor is actually jagged. As you shave these little zig zags get bent out of shape, and some almost break off. Like a hanging chad.

The linen on your strop works on a microscopic level as well. The tiny little fibers of the strop snags those little buggers and cleans the edge. The strength of the fibers in your linen will help determine how effective your stopping is.

At this point you get the canvas vs cotton vs wool vs poly rhetoric. They all do the job.

With that preparation the leather forces the jagged edge back into as uniform line as possible. The more uniform the line the keener your edge.

And THEN there's draw! Interesting topic as well.