Tamarian language

The Tamarian language was the spoken language of the Tamarians. The Tamarians spoke entirely by metaphor, referencing mythological and historical people and events from their culture. As a result, Federation universal translators – although they could successfully translate the individual words and sentence structure – were unable to convey the symbolic meaning they represented. Without prior knowledge of the Tamarians' history and legends, a word-by-word translation was of no use to someone attempting to communicate with them. This language barrier led to isolation of the Tamarian people after all attempts at communication had failed.

For example, instead of asking for cooperation, they would use a phrase such as "Darmok and Jalad at Tanagra", because their culture's stories include a tale of two Tamarians, Darmok and Jalad, who were brought together while fighting a common foe on an island called Tanagra. The problem with communicating in this fashion is that without understanding the meaning of the reference, the metaphor becomes meaningless. While explaining the structure of the language, Deanna Troi gave the example that "Juliet on her balcony" could be used to describe a romantic situation, but it is impossible to understand if the listener does not know who Juliet is, or why she was on the balcony. 

Some examples of the Tamarian language:
 * "Children of Tama" - Tamarian
 * "Darmok on the ocean" - loneliness, isolation
 * "Darmok and Jalad at Tanagra" - cooperation
 * "Darmok and Jalad on the ocean" - new friendship and understanding gained through a shared challenge
 * "The beast at Tanagra" - a problem to be overcome
 * "Kadir beneath Mo Moteh" - failure to communicate/understand
 * "Kiteo, his eyes closed" - refusal to understand
 * "Temba, his arms wide/open" - signifying a gift
 * "Temba, at rest" - when a gift being offered is declined
 * "Mirab, with sails unfurled" - signifying departure/engines to full/fleeing
 * "Shaka, when the walls fell" - failure
 * "Sokath, his eyes uncovered/opened" - understanding/realization
 * "The river Temarc in winter" - be quiet/silence
 * "Zinda, his face black, his eyes red" - anger or conflict, also can indicate pain or discomfort
 * "Rai and Jiri at Lungha. Rai of Lowani. Lowani under two moons. Jiri of Ubaya. Ubaya of crossroads, at Lungha. Lungha, her sky gray" - greeting between two different cultures/races
 * "Uzani, his army with fists open" - to lure the enemy towards you by spreading your forces
 * "Uzani, his army with fists closed" - to close rank and attack after luring the enemy
 * "Kira at Bashi" - to tell a story
 * "Picard and Dathon at El-Adrel" - successful first contact between two alien cultures, or to work toward a common goal

These phrases and idioms were often attenuated in conversation: "Shaka, when the walls fell" was heard shortened to "Shaka"; others followed a similar pattern.

Dathon also used "Kalimash, at Bahar" after experiencing pain in his shoulder, signalling to Picard with a hand wave associated with "stay back", or perhaps meaning "I feel better now" or "the pain is gone".

The first officer said "Kalesh, when it rises!" when the Enterprise tried to beam Picard back up and Riker tried to inform them that their own captain was under attack by the entity. Since the result was that the Tamarians closed the channel, it may have meant something along the lines of "Let them figure it out by themselves."

Background information
In one scene where Picard attempts to treat a wounded Dathon, the Tamarian says "Kiazi's children, their faces wet". It is unclear what Dathon means by this, although (since Dathon is trying to shoo Picard away from caring for his injuries at the time) it may allude to children crying for no reason; the Tamarian may be saying that Picard should not worry or feel sad, as nothing could be done. It might also mean that Dathon knew he was dying, as Kiazi's children apparently knew, since Picard was trying to find out the extent of Dathon's injuries at the time.

Apocrypha
The Tamarian language is explored further in the short story "Friends with the Sparrows" from the TNG anthology The Sky's the Limit. In the story, it is explained that Tamarians have a fundamentally different brain structure to most humanoids, and as such experience concepts such as time and self differently.

The story explains that Tamarian children learn the stories behind the metaphors, and thus their meanings, through enactment and repetition. Variations of meaning in metaphors were conveyed through subtle vocal and gestural cues that the universal translator had previously missed. In fields such as engineering and programming, a musical language was used to convey precise equations, numbers and instructions; thus explaining how Tamarians could effectively operate starships.