What does 僕 Boku mean?

Boku means I. So do several other words, and choosing between them tells a listener how the speaker sees themselves, which is information English has no way to carry.

The options, roughly

わたし (watashi) is the neutral, safe, formal-leaning choice, usable by anyone. おれ (ore) is blunt and assertive, strongly masculine-coded, casual to the point of rudeness in the wrong room. 僕 (boku) sits between them: masculine-coded, softer, often used by boys and by men who prefer not to sound like ore. あたし (atashi) is a casual feminine variant of watashi.

Beyond those there are regional forms, archaic ones, and pronouns that mark a speaker as arrogant, quaint or a child. The set is large and every member is marked.

The character underneath

僕 originally meant servant, and the humility in that origin is why the word reads as unassuming rather than assertive. Nobody using it today is thinking about servants, in the same way nobody saying goodbye is thinking about God, but the residue is audible in the register.

What translation loses

All of it. Every one of these becomes I, because English has one first-person pronoun and no alternatives to choose between.

So when a character switches, and characters switch, the moment vanishes. A boy moving from boku to ore is announcing something about who he now intends to be. A woman using boku is making a deliberate choice against the default. A character reverting under stress to the pronoun they used as a child is doing something a Japanese audience reads instantly and a subtitle cannot show at all.

How subtitlers cope

By moving the information elsewhere, when they can. Register can be carried in vocabulary and sentence shape, so a character who sounds blunt in Japanese can be made to sound blunt in English through word choice instead.

What cannot be recovered is the discreteness. In Japanese the choice is made once per sentence and is unmissable; in English it is diffused across a whole speech pattern, so a sudden switch has nowhere to land.

The point worth keeping

English speakers reveal self-image constantly too, through vocabulary, accent and syntax. The difference is that Japanese concentrates a large part of that signal into a single high-frequency word, which makes it both unavoidable for the speaker and invisible to translation.