The Enterprise encounters a planet that is an exact duplicate of the Earth, but a place where all the adults are dead, leaving behind children who age incredibly slowly ("one month every 100 years"). The problem: These children all have a disease causing them to die the moment they surpass puberty. The other problem: Kirk and the landing party have now contracted the disease, and must race against the clock in finding the cure before they die. Unfortunately, it's not much of race. "Miri" feels long, slow, and surprisingly uneventful (to the point where Kirk's speech near the end is particularly hard to sit through), and has far too many lapses in logic to make the emotional core ring true.
The notion of an "exact duplicate of the Earth" is put to absolutely no interesting use, and exists, apparently, for no other reason than so the plot could have a setting of "Earth, 1960." I had too many questions involving the children, like, just how is it they've managed to survive so long, yet don't have the capacity to grow beyond their childish ways? That's the paradox, and the story even acknowledges it at one point, but not effectively or believably on the given terms.
Still, just to hear Spock ominously say, "Without [the computer analysis of the vaccine], it could be a beaker full of death" [cue music of doom], makes it almost worth the hour spent.