Gameshark was the name of a line of cheating devices for various game consoles, manufactured by Interact. It was similar to the Game Genie, a cheating device for older systems that changed the game by patching.
There were versions for a multitude of systems, including the Game Boy and its little brothers, Playstations 1 and 2, Saturn, Dreamcast, and the Nintendo 64, which was both lauded for unlocking the massive amounts of hidden content in most of its games and reviled for its poor construction and buggy software.
For the cartridge-based systems, they plugged in the game slot and provided a slot for the game. When the console was turned on, it would boot to a menu where you could enable the codes, which could be activated with a switch once in the game. The cheats would let you get things like infinite lives, infinite ammo, secret characters, even let you open hidden menus. The codes themselves were in hex, and were basically instructions to change values (like 1 to 99). Because of the simplicity behind those kinds of codes, a few versions would let you make your own by searching the game's memory for choice values. To combat this, some games started using Dynamic Memory Allocation, which produced disposable codes that worked once, if at all. In response, better codes were made.
Unfortunately, Interact went bankrupt, and MadCatz bought the name, changing the Gameshark into a game save management utility. The spiritual successors of the Gameshark are Codebreaker and Action Replay.