When an Earth outpost is attacked and destroyed by a race called the Gorn, Kirk orders the Enterprise to pursue the Gorn ship with the intent of destroying it. In the midst of this high-warp chase, both the Gorn ship and the Enterprise wander into the territory of the powerful Metrons, who halt both ships and express their disdain for violent ways. The Metrons force Kirk and the Gorn captain to a planet where they must battle to the death using whatever primitive weapons they can find or create. The battle's winner's ship will go free; the loser's will be destroyed.
"Arena's" anti-violent, show-mercy-to-all message is heavy-handed, featuring a final scene that explains the message with the grace of a brick shattering on pavement. The use of Yet Another All-Powerful Alien Species™ to pass judgment on primitive humans is quickly becoming a cliché. In the meantime, the action sequences are laughably inept, even for late 60s Trek. Kirk's nemesis, the Gorn captain, never comes off as anything more than a klutzy man in a cheap rubber suit, performing "stunt scenes" that often have unintentionally comical results. (Ironically, considering the outdoor locations, it must've cost a lot of money to film this episode.)
The "cleverness factor" that is supposed to emerge from Kirk's situation doesn't pan out; Kirk's attempts to gain the upper hand with resourcefulness are undermined by bad pacing and a lack of suspense. And the notion of the Enterprise crew watching the entire fight on the viewscreen is both logically dubious and dramatically useless. The story scores a few points for being well-intentioned, but it was very poorly conceived.