Broad, as referring to a woman rather than something with great breadth, has less certain origins. It first popped up being used this way in the early 20th century. Theories as to its origin include simply referencing a woman’s broad hips, or perhaps from the American English “abroadwife,” which was a term for a slave woman, or just a woman who was separated from her husband.
Another popular theory is that it came from a slang term for a ticket, such as a train ticket, a meal ticket, a sporting event admission ticket, etc. This slang term became common around 1912 and by 1914 “broad” was being used, among other things, to refer to a prostitute, thus a pimp’s “meal ticket”.
“Broad” possibly came
to mean “ticket”, from the 18th century practice of sometimes
calling playing cards “broads”. This derives from the fact that
in the early 20th century, many types of tickets often resembled
playing cards.
This theory is attested in the 1914 work A Vocabulary of Criminal Slang, by Jackson and Hellyer where they define Broad as: Noun, Current among genteel grafters chiefly. A female confederate; a female companion, a woman of loose morals.
When “broad” first showed up as referring to a woman, it generally was used to signify a prostitute or immoral women. This gradually changed somewhat in the century since with “broad” slowly coming to be less used as a derogatory term and more used just to be synonymous with “woman”. One of the earliest instances of this was in the 1932 “Guys and Dolls”, where one characters refers to another as a broad without any negative connotation.
In the cases of “broad” and “slut”, there have also been recent efforts to “take back” the terms and spin them in a more positive light. For instance, in A Dictionary of Words About Women, by Jane Mills, a broad is defined as “a woman who is liberal, tolerant, unconfined, and not limited or narrow in scope.” “Slut”, while still retaining the same modern “loose woman” connotation, has begun to be a label worn proudly in some circles, though not without controversy.