I guess everyone here is pretty much correct. I will just add a bit:
A Paravane Stabilizer (also know as a flopper stopper) is in fact a device that slows the rocking from side to side on a boat. However, I find it is generally a term associated with full/semi-displaceement trawlers.
It was originally designed by the offshore shrimpers/trawling fish boats. It consists of two "poles" stretching off to either side of the boat. Long lines are lead from the poles down to what are commonly called fish (look like odd-shaped anchors). By presenting weighted "fish" that have the effect of pulling downwhen moving, the boat maintains an easy motion at sea.
Flopper stoppers are probably most effective while moving, but many people will tell you they work at anchor too. They are commonly employed on offshore trawlers and fishing boats, even today, with Nordhavn being one of the most recogninzed to use them. Here is a good example. THe fish are hanging on his transom:
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Many manufaturers of offshore trawlers have moved away from flopper stoppers (paravane stabilizers) in lieu of an active stabilization (versus passive stabilization). Part of the reason for this movement is the potential for a serious/deadly effect of losing one of the fish when they are both deployed, often causing the boat to round up and broach or heel so far to one side, it partially capsizes: The use of roll damping paravane systems (paravane stabilizers) - #15/2000 - Ship Safety Bulletin - Marine Safety
Active stabilizers, like the Naiad stabilizers (- Naiad® Marine Systems
) are like little fins that move up and down under the boat, keeping the boat flat in a rolling sea. However, these stabilizers only work while that boat is moving. They work well, but are prone to failure (as was reported on the Nordhavn rally from Fl to Gibraltar) and are quite expensive (around 25-35k, as I recall). Still, with the dangers and effort requires for a paravane, they may still be the best overall answer. In fact, Nordhavn has pushed away from reccomending paravane in lieu of Naiad's.
Hope that helps.