"First thus" describes the first appearance of a book in a particular new form: the first edition with a new introduction, new illustrations, a new publisher, a new format or revised text. It is the first of that version, not the first edition of the work.
How to spot it
Dealers use the phrase in descriptions, so watch for it in listings. On the book itself, look for clues that the text or presentation is new: an introduction or illustrations credited on the title page, a new publisher, a series name, or a copyright page that dates the new material later than the original publication.
What it does to value
A first thus is usually worth much less than the true first edition of the same work, because the work itself had already been published. It can still be collectable in its own right when the new element matters: the first illustrated edition by a famous artist, the first edition of a translation, or a fine press edition. The value then follows the new feature.
When a listing says "first edition" without qualification, check whether it is really a first thus. See first edition vs first printing, which compares these terms side by side.