This is quintessential Trek. Klingon agents beat the Enterprise to a planet with which our crew had planned to negotiate a mining agreement. The society they face is one in which the strong violently rule at the expense of the weak, and women are reduced to reproductive necessity.
"Is it not best to have two who bargain for the same goods?"
The leader of this society, predisposed to relations with the Federation, finds opposition among his ranks in an elitist who thusly challenges the leader to combat. This society hold combat "more pleasurable than love." This challenger, Maab, defeats the leader, Akaar, becoming leader himself.
In his total dedication to competition, be it physical in his combat or economical in his negotiations, Maab represents a certain unyielding absolutism. Whereas the previous leader may have been open to dealing with the more honorable group, this man is willing to accept any offer that is most beneficial, even if from the ruthless Klingons.
"He laid his hands on me, it is my right to see him die."
Maab orders the death of Akaar's pregnant widow, Eleen. Kirk's common swooning effect on female guest stars is turned on its head this week, as she orders his death at his slightest touch. In fact, though, the most fascinating and thematically revealing relationship in the episode is that of Eleen and McCoy, who takes her on as an unwilling patient as her delivery approaches.
"You said you were prepared to die, does that mean you prefer to die?"
"To live is always desirable."
On the run from the conflict-ridden township, McCoy attempts to care for Eleen and in doing so touches her pregnant belly. In what is initially a comic scene, she slaps him for doing so. Several times she protests with slaps before McCoy slaps her once back. It is this act that defines her ensuing affection for the good doctor, and evolution as a character.
His slap of violence shows her an equality in HER terms -- that of a society built on violence -- where usually she is subservient. In this demonstration McCoy is quickly able to juxtapose the inherent inequities of her upbringing. An upbringing which cruelly conditions women to have no connection with their progeny and full ownership given to the men after birth.
McCoy treats her as men treat each other in her society, allowing her grow as a character, transcending her previously defeatist expectations. (Wanting the death of her own child in light of her husband's death.)
"How'd you arrange to touch her Bones, give her a happy pill?"
"No, Right Cross."
The business with the societal conflict and Klingon presence are wrapped up nicely in the episode's sufficiently exciting climax. With the ultimate demise of Maab, reign is given to Eleen, who will act as leader until her newborn son (the rightful heir) comes of age. The Enterprise crew (owing most credit to McCoy's contributions on behalf of humanity) restored peace and equality to another self-endangering alien society.