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.
Rada's Blessing does not allow you to catch double big sharks.
For an exhaustive list of all known sources for this item, see here