What does touche' away mean?

Answer 1

"touché" is a term of "escrime" (Fencing), when one of the figher "touched" the other with the tip of his weapon. It counts as a point or a signal to reset the fight or something.

By extension, it came to mean that a speaker made a valid argument against someone else's argument. That person acknowledges the validity of it and the worthiness of the speaker.

Fencing is supposed to be a sport of gentlemen, putting a high value on the notion of honor and fair play, including acknowledging when you lose a point.

I don't know what the English word "away" is about in your question.