In order to move a vBulletin forum from a subfolder to the root directory for your web site content (e.g. public_html), you should move the forum files and the corresponding subfolders there.

Then open your vBulletin admin panel->Settings->Options->Site Name / URL / Contact Details and correct the forum URL in the corresponding field.

If you have a .htaccess file, check the paths in it and adjust them accordingly.