A regular playlist allows you to move songs around by dragging them. BUT, you can LOCK a playlist, so songs can't move. Click on the header of the playlist, next to the down arrow and you'll get a menu. On that menu you should see an item that says Lock or Unlock. If it says unlock, unlock it.
Now, if you're using a SmartList, you can't re-order those manually. The rules determine the contents and the ordering. But it sounds like you're using a regular playlist, so that's probably not it.
Brian.