As far as I know stropping will remove burrs, polish and align the edge, I have used plain leather, leather with polishing compund and with brasso, somebody once told me that I could use toothpaste but haven´t tried it. I have used my jeans, the palm of my hand, cardboard, newspaper (plain and with some brasso).
The effect of stropping will depend on many factors, how abrasive is the strop (or what you put on it), what kind of steel in the blade, how much force do you use, what condition is the edge to start with, etc.
On a smooth edge stropping can give you razor sharpness good for push cuts.
You may or may not want to strop a coarse edge, stropping on coarse edges will clean and align the toothy edge and take away some of the ripping effect (don´t use a good strop for a coarse edge since it will damage the surface of the strop, folded newspaper works well for this).