What does ¡que…! mean?

I said… — the que of insisting

A que at the start of a sentence, with nothing before it, says it again and harder. With the indicative it repeats what you said — que no, que ya voy; with the subjunctive it repeats an order — que te calles, que me lo des. It is how a request becomes a demand, and between people who know each other it can go back and forth several times.