Not the same Vanity Fair of current fame, this was a version published by The Commonwealth Publishing Company of New York City, incorporated in February 1902 but which went bankrupt in April 1904. "Vanity Fair" has been the title for at least 5 magazines, and as a phrase became popular through John Bunyan's Pilgrim's Progress where it was the name for Beelzebub's dominion, and later also as the title of William Thackeray's 1848 novel.
While France had a well-established men's magazine industry by 1900, America was just showing its ankles in 1903. A magazine called Vanity Fair (unrelated to the current incarnation) was the raciest thing around, and rooming house loozies the hotties of the time. In this New York, tabloid girls who drank like men might strip down to their petticoats and fall into bed together, exposing their corset cover and stockings to peeping male boarders. The famously loose morals of stage actresses made them popular subjects for these shenanigans, but the biggest thrill of all was bifurcation. "What?" one may well ask. Bifurcation, meaning "split in two", referred to the contours of a woman's legs revealed by her donning men's trousers. Bifurcation was a regular and very popular feature in Vanity Fair, it's popularity leading to Vanity Fair's Bifurcated Girls.
Although rather tame by modern standards, the sexual innuendo in this feature is rife. These 'risque' pictures of women in trousers are a strange precursor to a time when women would don trousers, not for men's titillation (as it seems here), but as a practical necessity when many took over 'men's jobs' during WW1 and WW2, and later simply because they wanted to.