If you are inferring to the ME part when in Nautilus and you select Permission for a file/folder, then this Me is simply a short way of saying your username. As seen on this image:
It is a simple way of showing the name. It means that in this case, the owner is you. In regards to creating another user and trying to take over files/folders from your other user, this will not work except if you use the
chown commands on it. As a matter of fact, if you created the other user, when you go into this user's home folder and see the permission on any of the files, you will also see ME as the owner, in this case implying that me is the other user.