The crew beams down to a world inhabited by people exhibiting strange behavior: a single-minded zombie-like trance state that explodes into temporary anarchy when "red hour" approaches. Kirk & Co. become involved in an underground movement to oppose the all-knowing Landru, a manipulative dictator that has apparently forced all of his citizens into uniform submission. Appropriately enough, Landru ultimately turns out to be a computer.
This episode is a metaphor for a lot of things, many of them approached with sophistication: anti-communist and anti-oneness sentiments, a warning of calculated technology replacing flesh-and-blood anticipation and adaptability, and the argued need for fighting authorities. But the plot flow lacks a cohesiveness to make it all come together into a unified, strong story with an underlying message. The "red hour" craziness is bizarre but confusing in narrative terms, and other small details of the plot are never fully developed.
Also, we have a slightly goofy resolution in which Kirk Outsmarts the Computer [TM] by feeding it some sort of circular logic that makes it fry itself and explode—arguments that just aren't convincing enough on story terms to be wholly worthwhile. Still, "Return of the Archons" has an intelligent underlying structure to it; it's just too bad the plot couldn't deliver on all fronts.