What are the desktop.ini files for?

As you make customizations to a system folder, the system will auto-generate a desktop.ini file in that folder to store the settings. A good resource for this is here. While you can delete the file, Windows will likely automatically re-create the file over time.

You are likely seeing two desktop.ini files because the Desktop is comprised of two folder locations. Your user's Desktop folder and the All Users/Public Desktop folder. There is likely a desktop.ini file for each of these folders. One is likely stored in .\users\some_username\desktop and the other is in .\users\public\desktop. It's impossible to have two files with the exactly same file name in the same folder.

In Windows 7, you can select 'Show hidden files, folders and drives' but keep checked 'Hide protected operating system files (Recommended)' to keep the desktop.ini and a few other items hidden from view.

http://msdn.microsoft.com/en-us/library/cc144102%28v=vs.85%29.aspx

Folders are normally displayed with the standard folder icon. A common use of the Desktop.ini file is to assign a custom icon or thumbnail image to a folder. You can also use Desktop.ini to create an infotip that displays information about the folder and controls some aspects of the folder's behavior, such as specifying localized names for the folder or items in the folder.

You probably have one in your desktop and one in the desktop for "All Users", thats why you see two files with the same name.