I typed a command to refactor my file from the current folder I was in to another folder.
What I wanted was: mv /var/backup /var/www/backup
However, I typed: mv /var/backup /var/www/
Now I can't seem to find my file anywhere! Is there a way I can recover it?

/var/www? It should be there as long as the/var/wwwdirectory existed. If it did not, your file has been renamed to/var/www.