The shuttle crew and an important commissioner are stranded on a planet by a cloud-like alien intellect.
I'd actually ignore the continuity of this episode with the tortuous use of Zephram Cochrane in the movie "First Contact", I frankly like the tragedy of the character as explained here much better. This episode is one of the first I remember backward and forward from the reruns of the early 70s, and it has some memorable aspects.
The idea of a completely "alien" alien in love with a human is intriguing and fairly remarkable for the series (and the late 60s) and its decently played here. It comes off as novel and sweet in most aspects. It is also interesting to see Spock, McCoy, and Kirk gradually discover the intent of "The Companion". The progressive ideas begin to falter when Kirk begins to stupidly spout how an alien can't love a human because sex ("joining") is impossible, but that's typical "Kirk-speak" - too bad it destroys the idea that by joining thoughts, the man and alien have already had more intimate relations than people are ever able to have. Those kind of ideas would have to wait for more sophisticated sci-fi. What many fans never realize, though, is that Kirk's stupidest dialog can often highlight an issue extremely well.
I actually like the staging of Hedford as changing in personality after joining with "The Companion" and in one clever scene, she uses the gueze of her costume to simulate glancing at Cochrane in a the same way as when she was a shimmering energy entity. The violin score introduced here works well, and becomes standard for some later episodes that introduce love.
I find this episode more interesting than many people give it credit for.