Corbomite was an imaginary substance invented by Captain James T. Kirk as a bluff against attack. Describing it as "a material, and a device, which prevents attack on us", Kirk used the corbomite bluff on at least two occasions.
In 2266, the USS Enterprise was captured by a vessel of the First Federation, Balok's massive Fesarius. Threatened with imminent destruction, Kirk seized upon the chance comments of Dr. McCoy and Spock for inspiration. On-the-fly, he "explained" the nature of corbomite to his opponent: that it reacts to any destructive energy that touches a Federation vessel, creating a reverse reaction that destroys the attacker. He went on to advise Balok that since the introduction of corbomite more than two centuries ago, no attacking vessel had survived the attempt. The bluff was successful, ultimately revealing Balok's power and belligerence were similar exaggerations. (TOS: "The Corbomite Maneuver")
A year later, Kirk and his senior officers were stricken with a hyper-aging radiation sickness, forcing the inexperienced Commodore Stocker to take command. Stocker brought the Enterprise into dire peril by ordering the starship into the Romulan Neutral Zone, inviting Romulan attack. By the time Kirk was cured, the starship was under fire from up to ten Birds-of-Prey. Kirk resorted to his corbomite bluff by sending a message to Starfleet in a broken code, warning that activation of the "corbomite device" would destroy the Enterprise and all matter within 200,000 kilometers, leaving behind a "dead zone" to be avoided for the next four years. The Romulans fled the area, allowing the Enterprise to escape. (TOS: "The Deadly Years")
Background information Edit
Corbomite wasn't featured in the first draft outline of "The Corbomite Maneuver" (when the episode had the working title "Danger Zone"). It was first referred to in the second draft of the episode's story outline, in which it was specifically said to be a substance that had been incorporated into the Enterprise when the ship had been made. Its detonation was said to cause a supernova and its uses purportedly included battle scenarios. When Balok left the Enterprise, the question of whether the substance actually existed was unclear to him.
Page 17 of the Star Fleet Medical Reference Manual describes corbomite as being an actual element (presumably a radioactive one) with the chemical symbol of Ct, an atomic mass of 361 for its most stable isotope, and an atomic number of 140, which Federation scientists had discovered on Starbase 27 in 2262.
The corbomite reflector was a special ability of Sovereign-class ships in the Star Trek: Armada and the Star Trek: Armada II PC games. It reflected enemy projectiles back to their point of origin, such as another ship and/or a torpedo turret or its equivalent, such as Romulan and Klingon plasma turrets. It is mentioned in-game as having been designed by Geordi La Forge, inspired by Kirk's famous bluff.
The alternate reality-set novel "The Assassination Game" portrays Kirk as having used a version of this bluff against Finnegan to avoid being "killed" by the latter in the aforementioned game. He claims to have accidentally made corbomite by spilling chemicals in the chemistry lab. According the Kirk, the substance absorbs the energy of anything that comes in contact with it and returns it several thousand or million times over. In addition, the amount he had created would supposedly destroy everything within ten kilometers of the area and create a dead zone for four years. The bluff is successful, but later, Finnegan confronts Kirk after having looked up corbomite and found that it didn't exist. Kirk tries (and fails) to convince Finnegan that his exochemistry teacher was the source of the bad intel.