Spock's parents, Vulcan ambassador Sarek (Mark Lenard) and his wife Amanda (Jane Wyatt), board the Enterprise for transport to a conference for Federation consulates. But trouble arises when a heated argument between Sarek and a Tellarite representative forms the basis for the suspicion of Sarek when the Tellarite later turns up dead—by way of an ancient Vulcan method. Meanwhile, the episode scrutinizes Spock and some of his life's choices, which has formed the uneasy rift between him and his father.
There are a lot of good uses of characters in "Journey to Babel," which has a plot that seems to go in every direction at once, yet still makes plenty of sense. In addition to the murder mystery, there's a medical emergency when Sarek suffers a heart attack and the only chance for his survival is an experimental surgery requiring a blood transfusion from Spock. Meanwhile, Kirk ends up in sickbay after being attacked by an Andorian. This puts Spock in command, who is forced to delay the transfusion because he must be on the bridge as an alien ship pursues the Enterprise with less-than-friendly intentions. Kirk slyly being a trouper and coming to the bridge to allow Spock to attend to his father is a humorous and very Kirk-like endeavor—especially after the crisis breaks out and Kirk finds he can't go back to sickbay. The murder mystery angle is maybe a bit unnecessary (Sarek is of course absolved), although it connects with the espionage angle involving the alien ship.
"Journey to Babel" probably has just a little too much plot, but fortunately this doesn't get in the way of seeing how Spock addresses his duty, his family, and the uneasy balance between his humanity and Vulcan rationality.