What do we mean when we say it today?
Nowadays, this phrase is used to send someone away, exactly as it was when Falstaff said it about the messenger. It's often used to rudely dismiss someone, or make it abundantly clear that someone is not wanted around anymore.
It's fair to say that this is one Shakespearean phrase that hasn't changed over the past 400 years. Shakespeare's audience would have understood this in the same way we do: sometimes you just have to give someone the boot.