The basic plotline of "Charlie X" is fairly simple. The Enterprise rendezvous (rendezvouses?) with a cargo vessel, the Antares, which has on board a teenage boy named Charlie; Charlie is the only survivor of a crash on the planet Thasus, having been marooned there since he was essentially an infant. They're to transport Charlie to a larger colony where someone will take responsibility for him -- perhaps he has surviving relatives.
Charlie exhibits the cluelessness you would expect of someone literally raised by ship's computers: no idea of how to behave around people, and minimal emotional maturity. He does seem to want to be liked and make people happy to some extent, but he's easily frustrated by the sometimes hard-to-grasp behavior of others. It is odd, though, that at first it appears the crewmen of the Antares are ill-at-ease around Charlie, and suddenly seem all cheerful and happy around him as they're bidding him farewell.
As time goes on, more "odd" things begin happening, ranging from Charlie offering Janice Rand (on whom he's clearly developed a crush) a gift of something that isn't available onboard, to the Antares exploding just as it makes what sounds like an emergency call to the Enterprise to warn them of... something.
In a sense, "Charlie X" is an inversion of the old "child raised by wolves" trope. Instead of a human boy raised by animals far below the normal human developmental level, Charlie has actually been raised by the Thasians, a tremendously advanced race (apparently evolved to the point of being bodiless intellects) who, in order to help Charlie survive on Thasus (which was not, in fact, really livable for human beings) made him into something between themselves and humanity; a boy with power to effectively "think" things into happening. Unfortunately they did not, perhaps could not, give him the wisdom and perspective to properly use this power, and so the end result is an apparently-adolescent boy who has the emotional maturity and reactions of a three year old. He really is eager to please, but he can also throw tantrums that have vastly greater consequences than any three-year-old.
Eventually, of course, Charlie's frustration with trying to understand people reaches the point that he decides he's just going to do things HIS way, leading to him making people "just go away" -- disappear Elsewhere -- control the Enterprise, and so on. In the end, however, Kirk, Spock, and McCoy realize that Charlie does have a limit: he can't control too many things at once, and so they start trying to overload his concentration. Their guess is correct but the outcome is potentially in doubt... when another ship suddenly appears nearby, to Charlie's horror.
It is, of course, a Thasian vessel; the Thasians apologize for the trouble Charlie caused and restore everyone he made "go away" or transformed. Apparently they cannot take away the power they gave, and so they will take him back to Thasus -- a prospect that horrifies Charlie because it's a desolate, lonely world, the Thasians (being bodiless) cannot touch him, nor, it seems, do they really understand human emotions. In the end, the Thasians take the crying, protesting, pathetic Charlie back with them, to protect humanity from a child with the powers of a demigod.
This is one of my less-liked First Season episodes. It's weak in several areas, some inherent to the plot, others more a result of time passage. Charlie comes across much more as a Creepy Stalker than he does a Nice Confused Boy, which would've been the better way to play it, at least at first; now that I think of it, he's sorta like Anakin Skywalker. I feel somewhat sorry for Charlie, but not as sorry as I think the writers wanted me to feel; Kathleen didn't feel sorry for him at all.
I'd forgotten how much mileage the original series got out of careful key lighting; here they use lighting to great effect for mood setting. The modifications in special effects aren't as clearly used here (the next episode uses them much more extensively). We see them playing 3-D chess for the first time in this episode.
Overall, not one of my favorite episodes, but still a very pretty restoration.