What does 1 Samuel 24:11 mean?

Look, my father, see this piece of your robe in my hand! I cut it off, but I didn't kill you. This proves I haven't done anything wrong or rebelled against you. I'm not trying to hurt you, even though you're hunting me down to kill me. 1 Samuel 24:11 - Modern Text Bible

(David shows Saul the piece of robe as proof that he means no harm and isn't guilty of rebellion.)