therefore, then, accordingly: a connecting word that draws a conclusion from what was just said and presses it on the listener
Toinun is a small connecting word, like "so," "then," or "accordingly" in English. It signals that what follows is the logical result of what came just before. In that much it overlaps with the far more common Greek word for "therefore" (oun). What sets toinun apart is a built-in nudge toward the person being addressed. It is built from two pieces, the second meaning "now" and the first an old word of direct address that carries the sense "I tell you, mind this." So the word does not merely link two thoughts in the abstract: it turns to the hearer and says, in effect, "so then, you see."
That extra edge explains why the word is rare and where it shows up. It belongs to formal speech and argument, the language of orators and debaters, and in the New Testament it appears only in its three most polished writers, in Luke, in Paul, and in Hebrews. Each time, it marks the moment a speaker turns to confront, exhort, or apply: Jesus throwing his opponents' own answer back at them, Paul turning the spotlight onto himself as an example, and the writer of Hebrews pivoting from teaching to a direct call to action.
The word is genuinely single in meaning. The differences from verse to verse, a dialogue's "well then," the opening of a personal application, a call to action, are differences of setting, not of definition. In every case it is the same inferential "therefore" with the same appeal to the hearer.