I have seen Puff used for Advert in crosswords before, but I don't think I've heard it used in real-life.
It's use number 8 here: puff [pʌf]
n
1. a short quick draught, gust, or emission, as of wind, smoke, air, etc., esp a forceful one
2. the amount of wind, smoke, etc., released in a puff
3. the sound made by or associated with a puff
4. (Life Sciences & Allied Applications / Physiology) an instance of inhaling and expelling the breath as in smoking
5. a swelling
6. (Cookery) a light aerated pastry usually filled with cream, jam, etc.
7. (Clothing & Fashion) a powder puff
8. (Business / Marketing) exaggerated praise, as of a book, product, etc., esp through an advertisement
9. (Clothing & Fashion) a piece of clothing fabric gathered up so as to bulge in the centre while being held together at the edges
10. (Clothing, Personal Arts & Crafts / Hairdressing & Grooming) a loose piece of hair wound into a cylindrical roll, usually over a pad, and pinned in place in a coiffure
11. (Clothing, Personal Arts & Crafts / Knitting & Sewing) a less common word for quilt [1]
12. (Life Sciences & Allied Applications / Physiology) one's breath (esp in the phrase out of puff)
13. Derogatory slang a male homosexual
14. (Life Sciences & Allied Applications / Plants) a dialect word for puffball