Gorn are physically much stronger and tougher than humans. A Gorn captain was able to shrug off a head-sized rock thrown into his torso, and a meter-plus boulder rolled off a cliff above him only stunned him for a minute. Similarly, he was able to lift a boulder nearly a meter in diameter and throw it at least several meters uphill.
While strong and durable, Gorn are not as agile or quick on their feet as humans; the Gorn captain's best speed was no faster than a brisk walk for a human, and Kirk was able to easily dodge most of the Gorn's strikes.
Nothing is known about the Gorn government save that it has the resources to construct powerful warships to defend the territory it claims.
The Gorn initially appeared in the TOS episode "Arena", in which a Gorn starship attacked a Federation outpost that was supposedly set up in their territory. They lured Kirk, Spock, McCoy and the Enterprise's tactical officers to the surface of the destroyed colony, where they ambushed the landing party, and their starship attacked the Enterprise with it's key command staff down on the surface.
Kirk was able to drive off the Gorn ground party with photon grenades found in the colony's armory. The Gorn starship beamed up their wounded and retreated. Kirk and company returned to the Enterprise and gave chase. The alien Metrons, another one-episode super race, interrupted the chase and attempted to end the dispute by having Kirk and the Gorn captain resolve their issues in single combat on an unknown planet.
This is the only time the Gorn appear in the main Star Trek universe, but another Gorn did appear in the evil mirror universe of the Terran Empire in Star Trek: Enterprise, in spite of the race appearing to be completely unknown to the Federation until Kirk's time.
The Gorn ship was able to withstand a full barrage of phasers and photon torpedos from the Constitution-class Enterprise, indicating defenses comparable to those of the Federation. The Enterprise needed to push its warp drive to its limits to overtake the ship during the chase.
Their infantry seems superior to that of the Federation (not exactly saying much), as they were able attack the Federation landing party from a distance of approximately 1200 yards. They were able to detect Spock's tricorder and use the signal to bracket the Federation position with explosive fire from a similar distance.
- ENT "In a Mirror, Darkly"