Simply copy (don't
move ) all the files in your demo directory up one level to the
You can do that in cpanel file manager.
To double check that you have done it properly change the name of the demo directory and make sure your site still works.
Once you have done that you can then safely delete the demo directory
[UPDATE] Also, don't forget you need to be certain your demo page is index.html or whatever the index page is named. This should replace your current home page.