The Enterprise crew members have difficulty communicating with another humanoid species.
When I try to think of an episode that is quintessentially Star Trek, I often think of Darmok.
The plot is is not particularly original as there are some similarities with 'Arena', but what makes it great is the use of the language barrier as the main obstacle for the crew to overcome. For me this is an example of a theme that feels uniquely Star Trek, particularly in the level of sci-fi detail combined with the hopefulness and progressiveness of the message.
Captain Picard has one of his finest episodes as the writers bring out the best of his intelligence and humanity to use for a heroic purpose. Commander Riker, Lieutenant Data and Counsellor Troi also have solid contributions to the story.
The concept of the Tamarian language is a fantastic idea as a puzzle for the main protagonists to solve. I'm not sure how plausible it is being used by a species depicted as advanced as this, but it works well as a story. Some people criticise the episode for this very reason and there is some merit to the argument, but personally I think it's been taken way too seriously in these instances. Most importantly the message about the importance of communication and understanding between people and across cultures comes through in a clear and entertaining way.
Visually it works very well as there is some quite cinematic storytelling, particularly in the scenes with Picard and Dathon.
Patrick Stewart and Paul Winfield are both fantastic with good support from the other cast members.
