Something that's published has been written, printed, and is officially for sale. Your family book of recipes is only distributed among family members — unless a published version makes it onto the shelves of your local bookstore.
A writer who's just starting out hopes for a published book — or even just a published story or article. Books, newspaper stories, and magazine articles can all be described as published, but so can online content like an essay or a blog post, or even a photograph on social media. The adjective published comes from publish, "issue for public sale" or "make publicly known." In the fourteenth century, it also meant "disgrace or put to shame."