A big shark is a large shark caught while harpoon fishing at any harpoon/big net fishing spot. Since players can only get it while fishing for sharks, it requires 76 Fishing to catch. Big sharks are a very rare catch (1/5,000), and catching one prompts the message "You catch an enormous shark!" instead of the usual "You catch a shark!"
It can be mounted in a skill hall in a player-owned house at 76 Construction. Before it can be mounted, it must be stuffed by the Taxidermist in Canifis, where she will charge 5,000 coins and return a stuffed big shark to the player. They can then mount the fish using 2 mahogany planks. When players take it to the Taxidermist, she will exclaim "That's quite a fearsome shark! You have done everyone a service by removing it from the sea!"
A big shark may be cooked into a regular shark for the standard Cooking experience. Catching a big shark will complete the elite clue scroll step given by Sherlock.
For an exhaustive list of all known sources for this item, see here