David Shiffman has a great article titled What shark finning means (and doesn’t mean): a primer and quiz.
Below is an excerpt, but be sure to read the full article at Southern Fried Science
Shark finning does not mean removing the fins from a shark. This is really important and seems to be a source of some confusion- not every shark fin for sale in markets is the result of shark finning! Shark finning means removing the fins from a shark while still on the fishing vessel and dumping the rest of the shark overboard. This is a problem because its wasteful (less than 10% of the weight of a shark is used), because its easy to quickly overfish a population even from a small boat (fins don’t take up a lot of space on board), and because its almost impossible for managers to know how many of each species were harvested. As stated above, this practice is also shockingly inhumane, as the sharks are often still alive when they are dumped overboard.