A giant carp is the result of cooking a raw giant carp, which can only be caught as part of the Fishing Contest quest. Level 10 Fishing is required, along with a fishing rod and red vine worms for bait — the latter can be dug up in McGrubor's Wood with a spade.
You can obtain multiple giant carps by fishing for them, and then dropping them and picking them back up (see drop trick). Once the quest has been completed, this fish can no longer be obtained.
Eating a cooked giant carp heals 6 Hitpoints. Cooking a giant carp gives no experience.