The Cold War
With a characteristic lack of subtlety, Star Trek VI uses the adventures of Enterprise to reflect some serious real-world issues. To be specific, the film employs the conflict between the Federation and Klingon Empire to comment on the Cold War between the United States and the Soviet Union. In particular, the film is interested in the collapse of the Soviet Union in 1991 and its consequences.
In Space, War Fights You
The parallels are plentiful. For instance, the Federation and the Klingon Empire are depicted as having wildly different cultures and political systems—as did the U.S. and Soviet Union. The biggest similarity, however, is that the conflict between Klingons and humans is defined not by massive D-Day style battles, but instead by simmering tension and political intrigue.
That's what made the Cold War "cold," after all. The Soviet Union and the United States never directly fought one another, but rather engaged in proxy conflicts and elaborate schemes of sabotage. Based on the evidence presented in The Undiscovered Country, we'd say that the same is true in the Star Trek universe. There's lots of intrigue, but there's not much actual combat.
Chancellor Gorkon, Tear Down That Wall
Further similarities can be found in the nature of the Klingon Empire's unfolding crisis. In the film, the Klingons are threatened by environmental pollution and military overspending. In reality, the Soviet Union was threatened by widespread poverty and political unrest. (Environmental pollution and military overspending couldn't possibly be problems in the U.S., right? Right?)
This forces the sparring partners to make a choice. Should they go for the jugular and finish off their foe? Or should they extend an olive branch in the hopes of building a better future?
Thankfully, the latter argument won out, both in real life and in the movie.
Of course, this is a vast oversimplification. The Cold War was a complex conflict, one that can hardly be boiled down to the "good guys vs. bad guys." Even so, The Undiscovered Country suggests that true peace can only be achieved with unity, when each side can respect the other's right to life, liberty, and all that jazz.