The sentence is grammatically wrong. So it doesn't mean anything.

Hey! Contrary to the "best answer", the sentence is fine. It's just more of a poetic grammar structure, found in poems, quotes, or proverbs. You could also read it like this: "He (who is) not busy being born is busy dying." I personally interpret the sentence as a way of saying that if someone isn't discovering new things, letting their creativity flow, or living life, they are dying. As Randy said though, there is no one way to interpret art :)

I think it means we should try new things, otherwise, we are just like waiting to die.

i think it means " you cant live and not die" in being born, you will die. so when the person is born, they are already dying. or something like that. it's an odd quote

Well, Bob Dylan is a poet and a prophet, or I thought so at one time. It could be interpreted as a challenge to us to continually be reborn, try new things, or die. Of course, it's art, so anyone can make their own interpretation.