The story centers on Captain Picard (Patrick Stewart) and Captain Dathon of the Tamarian race (Paul Winfield). The Tamarian language is unintelligible to Starfleet's universal translators because it is too deeply rooted in local metaphor, so its sentences do not have any meaning to other civilizations. When the Tamarians realize that this attempt has failed, the Tamarian captain has Picard and himself transported to the planet El-Adrel IV, which is occupied by a hostile entity.
While Picard and Dathon are on the planet, the crew of the Enterprise attempts to piece together some kind of meaning in the actions and words of the Tamarians. Via research, Troi and Data figure out the basic structure of the language, but, without the history of the metaphors, this does not lead to clearer communication. On the planet, through the use of situational knowledge and rudimentary sign language, Picard begins to understand the semantics of the Tamarian language, which is completely based on allusions to Tamarian folklore.
Picard and Dathon do battle with the dangerous entity inhabiting the planet, which results in Dathon's being mortally wounded. In an effort to communicate something of Earth's folklore to Dathon, Picard retells part of the Epic of Gilgamesh, concluding with Gilgamesh's mourning for his slain companion Enkidu, much like Picard's own sorrow at Dathon's imminent death.
During the climax, the Enterprise and the Tamarians open fire on each other. After Picard is transported back to the USS Enterprise, he is able to communicate with the Tamarians using their own metaphors and end the conflict.
The title of the episode comes from one of the metaphors Dathon uses: "Darmok and Jalad at Tanagra." In origin, this refers to the situation in which heroes must learn to trust each other so that they may work together to defeat a common foe. However, the phrase also speaks to the Tamarian's beliefs about captivity, combat, and relationships, as the phrase seems to imply by itself the inevitable forging of meaningful, positive ties between emissaries, should they also be comrades in a violent struggle.