From ShaveWiki
A strop is a length of material, usually leather or cotton, used to realign the edge before shaving.
Types
Hanging strops
The most common type of strop is the hanging strop. Usually made of leather or cotton it is a long rectangle of material. One end of the strop is hung from a hook or something else, while the other end is held and pulled taut with a hand.
Paddle strops
Loom strops
Materials
Leather
The most common, and most used, material for strops is leather. Leather provides a soft and smooth surface which gently aligns the edge of a straight razor. It is only used in both hanging and paddle strops.
Textile
The textile type of strop is often called linen, but few modern strops use actual linen. The most common material used is cotton. It is only used in hanging strops, not paddle strops.
Balsa
Balsa wood is sometimes used on paddle strops instead of leather.
Other
Recently Tony Miller of The Well Shaved Gentleman started producing a synthetic strop as an alternative to leather. The synthetic material is a nylon web core with a thermal polyurethane covering bonded to the core. Due to the material being non-pourous, it is not suited for use in a pasted paddle strop.
See also
Stropping with a Hanging Strop
Finishing with a Pasted Strop
Applying Paste to a Strop