Endorsement

A short quote from an author, expert, or public figure praising a book, printed on the cover, in the listing, or in the media kit. Endorsements are requested by the author or publisher before the cover is final. They are different from reviews, which the reviewer chooses to write.

The word blurb is often used for the same thing, and just as often for the book's description, which is a different thing entirely. Use endorsement when you mean the praise quote.