It's double negation — something that is not allowed in formal English, but is very common in informal English. (For example, in the _Rolling Stones_ song "I Can't Get No Satisfaction".)
What does it mean? It means exactly the same thing as the positive form would:
> No one knows what the morrow may bring forth!
Why did the author use the negative form here? I don't know. Possibly to give a more accurate representation of dialog, or possibly to give some indication as to the level of education of the speaker. It would take more context to figure this out.