Fugu is what the Japanese call some species of blowfish, also known as puffer fish. Its worldwide status as a delicacy derives mainly from the fact that eating it is risky. If prepared incorrectly, fugu can be lethal because parts of it contain tetrodotoxin, a poison that causes severe paralysis and respiratory distress, and can kill victims within hours. But it has a sought-after delicate flavor, it's a reported aphrodisiac and trying it gives you serious credibility as a culinary adventurer.
In Japan, chefs train for years to learn to prepare fugu properly -- and need a special license to do so. Which means eating it in a reputable restaurant is a (relatively) safe prospect. If you want to try it, make sure you're eating in a restaurant with a certified chef who has been extensively trained in the removal of the toxin-containing internal organs.