I just checked two of my books which are listed as hardcover.  They have shiny, plastic-y covers on top of the hardcover.    Are those library bindings?  If not, what IS a library binding?

The shiny covers indicate that the books are former library books.  They are still postable, and (unless I am totally off base, it's happened before)  you would still post these as hardcover. 

Library binding is a specific kind of hardcover, made sturdier to stand up to repeated use.  Usually a book with a library binding will have a different ISBN than the hardcover.  The shiny plastic cover (mylar, I am assuming) may be an indication that these are library books, but it isn't necessarily the case.  A bookstore near me sells those covers to put on your books to protect them. 

Whether they are actually ex-library books or not, listing them as hardcovers is perfectly fine.

Here's the Wikipedia listing about library binding:

http://en.wikipedia.org/wiki/Library_binding

The library binding I received for a hardcover was a little different as there was no dustcover, what usually showed up on the dust cover was actually printed into the cover. The plastic wrap is just a protector.

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