"The Corbomite Maneuver" is a title that refers to Kirk's gambit at the end of the episode. That, I'd say, is the lasting legacy of this one. It's basically a whole episode that explores his command style, and is highly recommended on that score.
It's also the second episode filmed after "Where No Man Has Gone Before," and as such is technically the debut for McCoy, Yeoman Rand, and Uhura (who wears a gold uniform!). Just in case you were wondering.
As with a lot of these episodes, there are precedents to be recorded. This is the first time a character ends up in the position of being asked to spend time with an alien who has been misbehaving because of their extreme loneliness. Some other examples of that include Star Trek: The Motion Picture, "Alter Ego" from Voyager, and "Exile" from Enterprise.
Speaking of The Motion Picture, there's a whole one-off character in "Corbomite" who serves as a direct counterpoint to Kirk, just like
Aside from Kirk's cleverness, his willingness to take a chance, which is one of the few direct character studies in the series and as such is essential viewing if you want to understand him as a whole, there's also the lasting image of the alien form the lonely alien takes, which was something viewers saw every week in the end credits.
So there's plenty to recommend about this episode. Not one of the greatest ever. But closer than a lot of the other early episodes.
And does Kirk ever reference corbomite again? You bet! Is it even real? Not a chance!
franchise * series * essential * character
Grace Lee Whitney
Memory Alpha summary