Where did this slang word for woman come from? Evidently, it is not from being broad in the hips as is commonly believed.
Broad originally meant a playing card, especially one used in three card monte. This usage dates to 1781 and may refer to style of playing deck. In modern card decks, a bridge deck has narrower cards than are found in in poker deck. If this variation in card size is older (I know words, not cards), then a broad could be a reference to this larger cut of cards.
By 1912, broad was also being used to refer to a ticket (admission, transport, meal, etc.). Why this is so is uncertain. It could be due to the resemblance between a ticket and a playing card, or there could be another reason.
By 1914, the word was being used to mean a prostitute (perhaps from a pimp's meal ticket), then to women of loose morals, and eventually to women in general. Another explanation for this last shift could be the use of cards in three card monte. The goal of that game is to pick the queen from among three cards, and broad could have transferred from the card, to the queen, to women.