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

1st thus : Indicates that this is not the first appearance of a book in print, but that this is the first appearance in a substantially different format than the true first edition. For example, a first illustrated edition of a book, or even a first paperback release of a book originally published in hard cover.

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.