"Do you really wish to know?" Spoilers from the books and/or games to follow!
The gentleman is to stand before the Ruler of the North and South. I must confirm that he knows how to bow. That, sir, is how you might bow to a whore on a street corner, not to the emperor of Nilfgaard. Please, watch. Leg extended, hand flat, head down, chin to chest...
If Geralt bows before the Emperor, when the emperor asks why he bowed since he heard Geralt bows before no one, Geralt explains that he bowed because he "didn't want to disappoint the chamberlain".
In the event the player refuses to bow before the Emperor, after the audience, Meredid will angrily chastise Geralt for not doing so and explains that he will be the one to receive retribution through lashes on Geralt's behalf.