The Enterprise is transporting several diplomatic delegations to a conference on Babel re: the future of the mineral-rich planet, Coridan. This ep introduces the Andorians and the Tellarites; later in the series, we learn that they are two of the four founding members of the United Federation of Planets. Among the passengers are Mr. Spock’s parents, the Vulcan ambassador, Sarek (Marc Lenard), and his human wife, Amanda (Jane Wyatt from Father Knows Best). There is obviously a chill between father and son. It turns out that Sarek is very ill w/ a heart condition; Dr. McCoy wonders if/how he can be saved. To add to the drama, there tension among the delegations; a spy is transmitting messages to a hostile ship which is following closely. When Capt. Kirk is wounded in an attack, Spock takes command just as his father needs a transfusion (that only he can provide)!
In the first ep ever to feature Spock’s parents (who are fan faves); Lenard received more fan mail than Nimoy for two weeks after this aired. We learn that Vulcans have a longer lifespan than humans. Being new to the show, Lenard and Wyatt asked Nimoy for advice on how the two of them could display their love in a subtle way. Nimoy suggested Sarek and Amanda touch and stroke each other’s hand by the index and middle finger. In S1 of TOS, Lenard (who was only 6 yrs older than Nimoy) played the unnamed Romulan commander in another terrific ep- Balance of Terror. Lenard had been a potential candidate for the recasting of Spock (when salary negotiations w/ Nimoy were going on at the end of S1).
Writer D.C. Fontana chose the name “Amanda” for Spock’s mother b/c it means “worthy of love” in Latin- how cool! She had become curious about past references to Spock’s background and fully fleshed them out here. Fontana also thought this would be an interesting way to reflect issues of the Generation Gap. Roddenberry wanted Kirk to be more involved with the story, so he wrote the scene where Amanda explains to Kirk about the rift between her son and husband. However, Fontana felt that it would be inappropriate for Amanda to discuss this w/ someone she had just met.
 …though there are some humorous moments, it’s mostly an episode driven by intrigue, suspense and interesting drama on the Vulcan side, where even more backstory is revealed on Spock…
Nimoy gives another subtly excellent performance; his demeanor is slightly different when speaking with his mother about the situation between himself and his father. Despite the Vulcan reserve, you sense his discomfort and sadness.
 The presence of Spock’s parents allows writers D.C. Fontana and Gene Roddenberry to further their character development of Spock as a man half-Vulcan and half-human. There are a number of wryly humorous moments between Spock and his father, who we learn not only have the normal Vulcan unemotional relationship, but who have some bad feelings towards each other. Maybe because they’re feelings, they don’t talk about it, and just ignore the situation as best as they can. Amanda… proves to be a surprising fulcrum balancing the two.
-Excerpts from IMDB reviews