A nudibranch is a mollusk, closely related to snails. While nudibranchs, or sea slugs, are soft and squishy without shells, young nudibranchs do have shells for added protection but shed them as they grow older. For protection, adult nudibranchs hide in rocks and coral reefs, but they do not live on them, they are swimming creatures. Some have colors that camouflage well with surrounding sponges and other life, while others have bright warning colors. This is because many secrete icky-tasting mucous or even toxins. Few nudibranchs eat smaller animals with nematocysts, or stinging cells, and can absorb those stinging toxins into their skin to defend themselves.
Naturally with the mention of coral reefs one would assume that nudibranchs are only found in tropical climes. However, I have collected about five different species of nudibranchs in Narragansett, Rhode Island, and that was just off the side of a dock. Nudibranchs range from the tropics to as far north as Canada, and are found all around the globe. They can grow less than an inch to 19 inches in length, depending on species. The Spanish Dancer is considered the largest species.
Nudibranch literally means naked gills. This simply means the gills are outside of the body, rather than held under flaps like with fish. These might be tough to spot on the more decorated nudibranchs, such as the Dorid Nudibranch, but on some species, they are quite easy to spot. The gills form a feathery ring at the posterior end of the animal. The points at the head end are not extra gills, nor are they devil horns. They are rhinophores. Yes, like "Tom's Rhinoplasty", rhino means nose, so these two horns are for sensing chemicals in the water. These chemicals could be warnings of predators, tantalizing scents of food, or the opportunity to reproduce.
Reproduction in nudibranchs is interesting. They are all hermaphrodites. However, they do not impregnate themselves, but cross-fertilize with a nudibranch of the opposite sex of whichever they are that day. After that, the female lays eggs, then both nudibranchs are free to change sex.
Information from personal experience, a class entitled "Marine Invertebrates of Southern New England" at the University of Rhode Island, and http://www.cybereef.com/nudiroundup/Pages/nudie_text.htm
For great pics, go to http://www.angelfire.com/mi/sharkcage69/nudi/chrom.html