Jasper: I don’t know if you should try jumping your bike off that home-made ramp. Are you sure it’s safe?

Fred: Of course I am. It’s perfectly safe.

Jasper: Famous last words.

Someone’s last words are the words they said immediately before they died, the last words they will ever say. If a certain phrase is often said right before attempting something dangerous (or potentially deadly), then that phrase would be common or well-known as “last words”. We use this idiom to imply that whoever just spoke is about to do something dangerous, especially when they have said something that commonly precedes dangerous behavior.