The Enterprise encounters a strange buoy sent out by an alien species in unexplored space. After destroying the buoy and proceeding forward, they also establish contact with the alien flagship Commander, Balok, who is well capable of destroying the ship. This is one of the earliest episode, so the sets, props, characters - Spock especially - and the general atmosphere of the show are a bit different than the later episodes, but that isn't really a problem.
What I personally love about this episode is the suspense, the encounter with the unknown. We get a good demonstration of what the Enterprise really is about, and a demonstration of Kirk's command skills (only rivaled by another season one episode, "Balance Of Terror"). Balok's mother ship, The Fesarius, is also quite beautiful!