One thing is fishery exports, but the Faroese also have the traditional Grindadrap, which is when they corral and kill pilot whales for meat, which is then distributed among the populace in a community effort.
The meat is strictly forbidden from being sold or used for commercial purposes, the pilot whale populations are carefully monitored to make sure they're not being endangered by the practice, and the whales themselves are carefully handled to try and make the ordeal as humane as possible. After all, if the whales disappear, they're not only losing out on a centuries-old tradition that's held very dear to most Faroese, but also an important source of food. The Faroe islands are hilariously unsuited to pretty much any kind of farming, so really the only other thing they've got is the sheep which are too few and too valuable as an export for the Faroese themselves to eat.
But no, they're actually all crass, thick-skulled barbarians who murder "the famous and intelligent Calderon dolphins" (not an actual animal) for sport and glory. As such, they've been very popular targets for groups like Sea Shepherd, Greenpeace and PETA. Eventually they got fed up with Sea Shepherd coming in and vandalizing public and private property and harassing people, so they were registered as a terrorist organization and any direct affiliation with the group will land you an immediate deportation.
A few of you might actually remember the Calderon dolphin thing, it was this viral email thingy that was making the rounds a long time ago. I think the original, horribly written and completely nonfactual website is still up and running...