Worf's son Alexander reaches the age for the Klingon Rite of Ascension, in which he can begin the journey to become a Klingon warrior. Worf of course wants Alexander to follow in his traditional Klingon ways, whereas Alexander is understandably reluctant, having never been all that enthusiastic when it comes to Klingon stuff (I guess that's probably an understatement). But Alexander is not completely unreceptive, especially after Worf reframes the dialogue by taking him to a nearby colony and immersing him in some Klingon culture.
"Firstborn" is notable in that it treats Alexander as a halfway plausible child rather than an annoying cliche or plot convenience. I can't stress how much that's in the show's favor. Whereas most Alexander-centric episodes tend to be dead on arrival, this one shows Alexander as a child trapped between cultures with his father steering him in a direction that might not be best for him. On the other hand, I'm not exactly singing this episode's praises; the Klingon material is standard-issue fare, and there's the matter of that bizarre twist at the end. (And I guess this too qualifies for the season's Family Tree Theater sweepstakes.)
The crux of the story revolves around a character named K'Mtar (the reliable guest actor James Sloyan), who helps Worf fight off an assault on the Klingon colony and says he's a loyal friend of Worf's brother Kurn. He offers to help Worf bring Alexander into the Klingon fold. This results in the aforementioned standard-fare Klingon dialogue, before we get the turning point where Worf and K'Mtar push too hard to get Alexander to kill a holodeck opponent in a bat'leth combat simulation, prompting Alexander's revolt. (Lesson for Klingon parents with partially human sons: Some pre-adolescent children don't actually want to kill people.)
Some plot details arise (obliquely involving the Duras sisters and a knife in K'Mtar's possession) which leads to the revelation that K'Mtar is actually an adult Alexander who traveled back in time 40 years to convince his younger self to become a warrior rather than a peacemaker — in order to avert a sequence of events that will result in Worf being killed. Adult Alexander decided that if he can't change his past he'd kill himself as a child (sort like the premise of Looper in reverse).
There's a tortured character at the center of "Firstborn" — so much so that he's willing to undo his own existence (not to mention unleash untold contamination upon the timeline) in order to save his father. This is, to put it simply, a stretch. We're supposed to believe that time travel is such a casual device that it can be used to rectify personal demons (why isn't everyone doing it then?) and that adult Alexander feels so guilty about his father's death (who would be something like 80 years old by that time) that he believes he himself should die for his life's choices? Wow.
On the one hand, there's decent character work here, where this extreme and bizarre scenario makes Worf realize just how much Alexander needs to choose his own path rather than being marched down the path of warrior-hood. (And there's a haunting scene of well-utilized continuity where adult Alexander recalls the night of his mother's murder.) On the other hand, the logical/emotional arc of the adult Alexander is so pathetically sad as to be absurd. It's just really hard to swallow this character's motivations. Part of you wants to shake the guy and tell him he has to live with his life's choices (which were honorable on their own terms). One wonders if "Firstborn" might've been a better final outing for Alexander without the central sci-fi twist that it was clearly sold on.