What does F. Scott Fitzgerald mean when he says that Tom and Daisy belong to "a rather distinguished secret society"?
Iin chapter one at the dinner party with Tom and Daisy Buchanan and Jordan Baker.
I agree with both of these answers but would like to add that it is also a reflection on Gatsby's wealth. Tom and Daisy are not just super rich, it is old money. They were both born into class and privilege and do not know what it is like to have to work for their money unlike both Nick and Gatsby. If we were to compare them to their place in English society, they would be right up there as branches on the royal family tree.
From their esteemed position in society, Tom and Daisy look down on and have contempt for everybody, including the new rich like Gatsby. Since he was not born to wealth, he displays it ostentatiously. This is amusing to the old money, the distinguished secret society.
Daisy clearly suggests the lines of societal distinction in this excerpt. The "secret society" at which Daisy hints is the ultra-wealthy class, one to which Nick does not belong. Although he has experienced certain "privileges", as evidenced by his early narration in Chapter One, he has not made entry into the wealthy class to which Tom and Daisy Buchanan belong.
Interestingly, this reference may parallel the author's own perspective. Consider this quote from Fitzgerald: "That was always my experience—a poor boy in a rich town; a poor boy in a rich boy's school; a poor boy in a rich man's club at Princeton.... However, I have never been able to forgive the rich for being rich, and it has colored my entire life and works."
Nick is the speaker here. The entire quote reads, "I waited, and sure enough, in a moment she looked at me with an absolute smirk on her lovely face as if she had asserted her membership in a rather distinguished secret society to which she and Tom belonged."
This is a class-distinction remark. Nick is not as well-too-do as the Buchanans. Daisy gives him a smirk to let him know this. She has been friendly to him, but their stations in life are vastly apart.