Leather strops are excellent for removing scratches and polishing edges to a mirror-like shine.
The syringes shown in the product image are the diamond paste, which should be applied to the leather strops. You only need to apply a tiny bit if paste to the leather, and then spread it around so it coats the whole surface of the strop with a thin coat. Once you apply the paste, it's good for about 30-40 knives before you need to reapply it, so the paste will last quite a while.
Stropping removes the micro-serrations from an edge, which actually decreases cutting ability for most cutting applications. The time when a stropped edge is superior is when the knife is used for push-cutting, where the blade is being pushed into the object being cut, as opposed to pull-cutting, where the blade is drawn across the object being cut. A stropped edge is also superior for cutting through soft meats, where you don't want the micro-serrations to slightly shred the meed as the blade cuts. Cutting sushi-grade fish is an example of this.