Here's Bruce Robert's description, from Passage Maker:
'Flopper Stoppers' is the name generally given to a device that has been successfully used by long distance powerboats to reduce rolling. The rig consists of one pole each side of the vessel that is pivoted at or near deck level. The poles are rigged with guy wires so allow them to be swung out at right angles to the vessel and parallel to the surface of the water. Twin triangular devices of about 1 sq. ft / 0.09 sq. M each are suspended by wires from the poles so that the 'fins' are sufficiently below water level to act as stabilizers. The rig generally resembles that seen on prawn or shrimp trawlers except the boards are replaced with the fins.
Apparently, they're not very commonly used on sailboats.