2 Answers

The narwhal's tusk isn't unique at first glance. Elephants, rhinos and walruses all have these long, protruding teeth. But this one is different from any other tooth you've ever seen.
Contemplate your own teeth for a second. We usually only think about them when there's something wrong -- a chip, a cavity, discoloration. But teeth themselves are incredibly durable, able to survive fire and outlast the rest of your body after death. Teeth are hard, which makes them useful for their main purpose in humans: chewing food. On the outside of the tooth, there's enamel, with hard materials called dentin and cementum below that. At the very center of the tooth is the pulp, where the blood and nerves are. (You might realize you have a cavity once the pulp is infected and hurts.) The hard outer layers protect the sensitive inner layers of the tooth.
A narwhal tusk is the exact opposite. The soft, sensitive part is on the outside, while the dense, hard part makes up the middle. Ten million tiny holes lie right on the surface on the tusk. Human teeth have these little tubules too, which is why sometimes the cold bothers your teeth, but they're covered with enamel. Imagine having all your nerves exposed in the icy waters of the Arctic. Why would the most sensitive part of a tooth be on the outside?

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On the anterior end of the Narwhal, hopefully not in your posterior while trying to get one.