It confused me at first as well.
Think of it this way.
The LIBRARY is where everything is saved and permanent.
The Editdesk Library is where you bring in elements/clips from the library on to your desktop/source area to work with.
I can copy, edit a clip in the timeline or source area. I can even delete it. But the MASTER of the clip still resides in the Library.
It can only be delete from the framestore, if you delete it from the Library and there are no other 'living' copies on the editdesk.
Some clips on the editdesk can have new material, like a CC clip or something you made in Action. These clips only exist on the editdesk, they don't exist in the main Library. So if you were to delete a clip you made in Action and it had not been saved in the Library, then it would be gone.
The editdesk library can also be used for organization. You can sort clips into source areas, name them, have different record areas. You can then SAVE your entire Editdesk to the Library and you can then clear your Editdesk, and you are able to reload it again, from the Library.
Libraries are also seen form project to project, so you can clopy clips from one project to another, and in 2011, they made the editdesk also available in the Network.