Hi, John - My Joy of Cooking cookbook says "Finnan Haddie" is smoked haddock, a fish that may be broiled (basted in butter), or baked.
My dictionary says it's literally haddock of Findhorn, a fishing port in Scotland.

Barry Finn, who used to be around here much more often, was in a singing group called "Finn and Haddie." I had no idea of the meaning of "finnan haddie" until I'd heard the name of Barry's group.
Now you know.
-Joe Offer-