Flukes are parasitic flatworms of the phylum Platyhelminthes, class Trematoda; they're related to that other yucky parasite, the tapeworm.
This is going to be gross, so prepare yourself. Flukes possess disks with which they cling to their host by sucking on; they have an external cuticle rather than an epidermis in order to resist being digested by the host. These darlings usually ingest food in the way you'd expect, though some species have no digestive system at all, absorbing food through the cuticle. Flukes are usually hermaphroditic, though they reproduce sexually. One fluke can apparently produce over 500,000 embryos. And all this is giving me a creepy vision of blood-sucking fingernail-covered perverted worms.
Well. There are many orders of fluke. Monogenea are external parasites which live on the gills of fish. Digena are internal parasites, 35 species of which are known to live inside humans, often after passing through various animal hosts on their way to us. Let's see: there's the lovely liver fluke, Clonorchis sinensis, which passes through snails and fish on their way to humans, who become host to this baby after eating infected raw fish. The flukes shed eggs which pass out of the human host via their feces to begin the cycle anew; these charmers are prevalent in East Asia. There's another liver fluke too, Fasciola hepatica, which passes through snails and encysts on grasses, and which causes fatal liver rot in sheep and other herbivores who happen to munch them down. Then there's the suave blood flukes of the genus Schistosoma, common in Asia and Africa, which cause schistosomiasis by burrowing through the skin of humans and animals and lodging in the blood vessels. The delightful lung fluke of East Asia passes to humans via uncooked crab meat, settling in the lungs. Gack. In case you think this is a "third world" thing, there's a species of fluke in American lakes which causes of rash called "swimmer's itch". Better an itch than a rotted liver, though, I guess.
Fluke is also used to refer to certain species of flatfish (flounders), and to an accidental advantage or stroke of good luck. God knows why, with all those flatworms around.
Thanks to infoplease.com for gory details.