The Friends of Narnia dinner sees many of the different characters from the Narnia series gathered together in one spot. The magic rings the Professor describes in this scene are important objects in the first chronological entry of the series,
The Magician’s Nephew. The Professor wants to get his hands on the rings again because they have the power to transport their wearers between worlds, and he hopes to heed Tirian’s call for help. The Professor ability to know that Narnia was in danger in the first place implies that there is a powerful bond between the two worlds, perhaps one that is spiritual in nature.