The Enterprise is going to investigate what appears to be a very slow-moving viral form of mass-hysteria which has, over centuries, brought several thriving civilizations on many different planets down. Spock reviews the epidemiology of the phenomenon at the beginning of the episode, revealing that the trajectory of the epidemic places a Federation colony directly in its path. Sam Kirk, his wife and their son, live in this colony.
Captain Kirk is directly affected by his family's involvement in all of this, and Shatner does a very nice job of portraying a captain whose professionalism and rational judgment are threatened, and whose usual rational support structure (Spock) is also imperiled and unavailable. In a scene which was, unfortunately underexploited by the mediocre script, Dr. McCoy rises to the occasion and, surprisingly, fills both his usual role and that of the great first officer.
Herschel Daugherty directs this memorable episode of TOS, and does an admirable job with a somewhat weak script. The Stephen Carabatsos script creates some problems for the acting (particularly Nimoy, Barrett and Kelley), and - like his previous effort "Court Martial" - makes the pace a bit inconsistent. Kelley and Shatner are truly remarkable despite these challenges.
The episode also uses setting very nicely, with a very minimal use of backdrops and carefully chosen locations for rare open air shots. Additionally, Spock's character is very nicely examined, the developing rivalry and friendship between McCoy and Spock is enhanced, and the powerful - though unresolved - relationship between Christine Chapel and Spock begins. Finally, this (and the great earlier City on the Edge of Forever)is one of the first episodes to exploit the (unfortunately largely overlooked and unrecognized) subtlety of William Shatner's acting ability by placing Kirk's personal life in the way of his professional practice. This became a major theme as the series continued into its 2nd and 3rd seasons.