During Jay Gatsby's lavish parties in "The Great Gatsby", illegal activity mostly centers around the consumption and distribution of alcohol, specifically in the form of a speakeasy.
The novel is set during the Prohibition era in the United States (1920–1933), a time when the manufacture, sale, and transportation of alcoholic beverages was strictly forbidden across the whole country. This was as a result of the 18th Amendment to the United States Constitution and was enforced by the Volstead Act.
Despite this ban, illegal speakeasies (hidden bars and clubs selling alcohol) were ubiquitous, and many households would sneakily enjoy drinks. Gatsby's parties, too, were rife with freely available liquor, which he distributed in plain sight of all the guests.
The flow and availability of alcohol at Gatsby's events were largely thanks to his connection to criminal activities and their perpetrators, covertly suggested in the novel to be his business relations with Meyer Wolfsheim, who is associated with organized crime.
This illegal activity not only underscores the decadence and societal corruption of the Roaring Twenties - a central theme in the novel - but also enhances the sense of danger and allure surrounding Gatsby himself.