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In order to implement this you can create a new folder content type and add an order column to this content type. You do need to have the appropriate rights to do so.
The steps would be as follows.
- Go to Site Actions
 
- Go to Site Settings
 
- Go to Site Content Types
 
- Click Create New
 
- Give it a name such as Folder Order
 
- Select Parent Content Type from as of Folder Content Types
 
- Select Folder as the Parent Content Type
 
- You can create a new group or leave it in custom content types
 
- Click OK
 
- At the content type settings click Add from new site column
 
- Create a site column called Item Order or something similar, select the type as Number
 
- Click OK
 
- Go to the list where you want the folders to be ordered
 
- Go to the list settings
 
- Go to Advanced Settings
 
- Select allow management of content types
 
- Select No for display new folder command on the new menu
 
- Click OK
 
- You should now see an area called content types, leave the document as is
 
- Click Add from existing site content types
 
- Select the Folder Order (or whatever you named it)
 
- Click OK
 
That's it you can now create a folder structure with the order column and order your items as you need.