Starfleet, on the verge of war with the Klingons, sends the Enterprise to the planet Organia to negotiate a protection settlement so the Klingons won't invade the planet and set up a base there. But these people want nothing to do with the Federation or their protection—and they're convinced that they aren't in any danger. Kirk is furious when these Organian "sheep" refuse to stand up for their own way of life. The Klingons, led by Kor (John Colicos), subsequently arrive, take Kirk and Spock hostage, and threaten to subject them to a rather nasty mind probe to extract Starfleet war information.
This story finds irony in its plot, as Kirk is determined to convince the Organians to turn to violence, even though Starfleet's mission is supposedly one of peace (this is a story suited particularly well to Captain Kirk's adamant boldness). The Organians' claim to ultimately safety is proven when they turn out to be powerful beings capable of stopping at will the war between the Klingons and Federation.
The use of all-powerful, superior beings to preach a message of anti-violence to lowly humanoids is a theme that's been grossly over-utilized in Trek's freshman season, but fortunately the usage here is far better realized than in, say, "Arena." Kirk arguing vehemently for the right to engage in war is particularly telling.