Nick Caraway meets the man with the enormous owl-eyed spectacles in Jay Gatsby's library, during one of Jay's parties. Nick and Jordan had politely left their company to find Jay. The man was drunk and wanted to know what Nick and Jordan thought of Jay's enormous collection of books.
The man seemed overwhelmed by the idea that Jay actually had real books in his library and not just mere cardboard replicas to create the impression of reality. His comment that Jay is a "regular Belasco" is a reference to a famous and popular playwright, impresario, director and producer at the time, David Belasco.
The reference to one rooted in theatre implies firstly, that the library has the makings of a theatre - it is impressively large and well-stocked. Secondly, it suggests that Gatsby is putting on a show. This is the reason why the man with the spectacles is so surprised that the books are actually genuine. He expected them to be fake. Just as the room presented something theatrical, so should the books have too.
It is ironic that the man should make this comment because he accurately identifies the theatricality and artificiality of Jay's life without realizing it. The Jay who presents himself to his audience is not the real James Gatz. He has adopted a fake identity and affectations such as "old sport", to impress and convey an image of wealth and academic success.
Furthermore, the reference to the owl-eyed nature of the man's spectacles alludes to knowledge, deep scrutiny and investigation. The irony is however, that the man makes the remark whilst drunk, so even his insight is doubtful since this is the type of logic or rationalization one can expect from an inebriate. His remarks are the ramblings of a drunk and are of no consequence or import.
Throughout chapter 3, many presumptive details are given to portray the various shades of Gatsby. Rumors fly around about his service in the army, his education at Oxford, and his business. Some even suggest that he has killed a man.
The reference to Belasco that comes from the Owl-Eyed man is very significant for several reasons. First, David Belasco was a famous actor, playwright, and producer. Owl-Eyes is suggesting that Gatsby can put on quite a show. Owl-Eyes is also saying this while very drunk. Many people's inhibitions drop when they are drunk, therefore, he may be telling a truthful tale after all of the potential lies readers have read throughout the beginning of the chapter. Furthermore, the simple symbolism in his name suggests that he might be able to see something everyone else does not.