If you give something your imprimatur, you give it your formal support or approval. An imprimatur is a fancy version of a thumbs-up sign.
Originally, an imprimatur was a license that permitted a book to be printed. This word still has the meaning of official or public approval. When the president signs a bill, he gives it his imprimatur. You might give your imprimatur to your favorite rock band by wearing a t-shirt with the band’s logo on it.