One hasn't been on the site before, and the other has. Depends on the context - generally it's evaluated by dropping cookies.
A new visitor is also called a unique visitor. She/he has never seen or heard of your site before. A returning visitor is somebody who either likes your site enough that she/he decided to come back or made a horrible mistake by accidentally visiting it again.
Answer already in their question so what I can explain, Its better you can see meaning of word "new" and "returning"