Because the Tamarian language was based upon a series of metaphors, prior attempts to communicate verbally had failed. Knowing this, Dathon beamed himself and Starfleet Captain Jean-Luc Picard down to the planet, where he hoped that some time together would better help them understand each other's languages. At first, Captain Picard believed Dathon had kidnapped him and when the Tamarian offered him his dagger, Picard assumed he wished to engage in combat and thus refused. In reality, Dathon was offering Picard a weapon to defend himself against an electromagnetic lifeform that resided on the planet.
After a short time on the surface, the lifeform attacked the two men, wounding Dathon. Picard was able to fend off the creature and tend to Dathon's injuries. It was during this time that Dathon was able to "teach" Picard how his language worked - using metaphors; proper names and places Dathon cited were references to situations in his history. Armed with this new found understanding, the two were successfully able to communicate on a basic level, which assisted in defeating the creature a second time.
However, this victory came with a price as Dathon was mortally wounded. But his sacrifice was not in vain, as when Picard returned to the Enterprise, he was able to successfully communicate with Dathon's ship and explain how their captain was killed, thereby opening a new era in relations with the Tamarian people. (TNG: "Darmok")
Because Paul Winfield was a large man with a great presence, the makeup department realized that building alien features up through separate appliances would enlarge his head too much. So, instead, the department built a single piece that covered the actor's entire head and featured a bony ridge, almost like a central skull spine, over the top of the Tamarian's head down to his nose, which was more like a snout, and bony ridges on both sides of his skull. The three ridges looked like three parallel tracks of bone connected by a set of ridges that ran across the top of his head and down the bridge of his nose. His ears were large, but recessed, and there was a separate appliance for Paul Winfield's upper lip that was modified for the other actors portraying Tamarians on their ship. The Tamarian coloring was added with hand-painted patterns of orange spots in patterns that were unique for each individual Tamarian, although they were all modeled on Paul Winfield's pattern. (Star Trek: Aliens & Artifacts, p.121)
The script for "Darmok" states the pronunciation of Dathon's name is "DAY-thahn." Additionally, it says of the scene in which Dathon first appears; "displays a TAMARIAN -- CAPTAIN DATHON -- flanked by his FIRST OFFICER, and TWO OTHER OFFICERS. Their uniforms are rich with insignia -- and each wears a small ceremonial dagger across his or her chest. But all look the very embodiment of "well-meaning." 
The novel Articles of the Federation references the events of "Darmok" and how the progress made since that time was considered one of the noteworthy accomplishments of Federation President Jaresh-Inyo and his administration.