bigons ere things of the past,things that have "gone by". It means let things that are in the past remain there. It does no good to bring them up now. Forget bad things and move on with a positive attitude.
let bygones be bygones means forget about it and start from a clean slate. let the past be the past. if you look at the word it even makes sense. by gone .. things go by, they are gone. they are the past.
Let things that have gone by (bygones) stay in the past. Let them go and stop bringing them and rehashing them. This is used when someone keeps mentioning a wrong another person commuted a long time ago.