The meaning is the same as 'next day' but with emphasis. 1. We should hang out the next day you are free. 2. We should hang out the very next day you are free. The meaning is about the same, but #2 sounds more important.

thXxXx guyZz

When I was in grade school, they taught us a song called "The cat came back" -- I think it will answer your question :)