The narwhal (Monodon monoceros) is a smallish (3-5 meters long) member of the cetacean family chiefly found in Arctic waters. It's unique among marine mammals in that it has a single long tusk sticking out of its front end. The tusk is the whale's left upper incisor tooth, and grows forward, spiraling around to form a pointed lance about 2 meters long.
There was once a fairly lively market in narwhal tusks, because they matched the popular image of the horn of a unicorn. Since the unicorn's horn was believed to be an infallible remedy against poison, various affluent paranoids among Europe's nobility bought narwhal tusks until about the 18th Century. By then the true nature of the narwhal's tusk was becoming well-known and the nobles of Europe were becoming more worried about guillotines than poison. Many old "unicorn horns" can be seen in European museums, including a remarkable poison-neutralizing unicorn cup in the Vienna Kunsthistoriches Museum.
But the reason why the narwhal has its tusk was not really known. One theory early on was that the narwhal used its tusk as a weapon. In Jules Verne's 20,000 Leagues Under the Sea, Captain Nemo's mysterious submarine is first identified as a giant narwhal when it rams a steamship.
But not all narwhals have tusks, which means it can't be essential for feeding. Since male narwhals have them, another theory was that it was used for mating battles -- the marine equivalent of a stag's antlers. Indeed, male narwhals have been observed rubbing their tusks together, which was interpreted as a kind of cetacean "fencing." Trouble is, some tusk-bearing narwhals are females, which kind of blows the whole mating-battle theory out of the water.
Recently Dr. Martin Nweeia, of the Harvard Medical School's dentistry department (really!) did some serious examination of the internal structure of narwhal tusks and found something very interesting indeed. The tusk may be a sensory organ.
Apparently narwhal tusks are filled with sensory nerves, up to 10 million or so, and can provide the whale with information about water temperature, pressure, and salinity. These may help the narwhals navigate in polar water and find prey. (This doesn't explain what the male narwhals are doing rubbing tusks, though -- maybe it just feels good.)
There's an interesting parallel in aerodynamics: high-performance jet airplanes, especially experimental models, are often fitted with a Pitot tube at the nose. The tube isn't just to make the plane look extra-pointy; it carries pressure sensors and puts them out in front of the disturbed airflow created by the body of the plane to determine airspeed. The narwhal's tusk may do much the same, putting water sensors out where the whale itself doesn't interfere.
Dr. Nweeia's research still leaves some questions: why don't all narwhals have tusks? Is there some unique feature of the narwhal's life which makes it an advantage? It would be interesting to see if swordfish bills have a similar sensory purpose.