wraps : The paper covering on the outside of a paperback.

dust jacket : A protective and often decorative wrapper, usually made of paper which wraps around the binding of a book.

trade paperback : Often used to indicate any paperback book that is somewhat larger than a mass-market paperback.

reprint : Any printing of a book which follows the original edition. By definition, a reprint is not a first edition.

As New : "the book is in the same immaculate condition in which it was published. There can be no defects, no missing pages, no library stamps, etc., and the dust jacket (if it was issued with one) must be perfect without any tears." Condition definition from AB Bookman's Weekly.