In the western US, it generally means furnishings are included; in rentals and some vacation properties it may also include kitchens with pots, pans and dinnerware; linens and towels too.
In the eastern US, "turn-key" is often used to describe a home that has requires no immediate repair or work to inhabit by the new owner. If you see this word used in a listing - ASK THE LISTING AGENT EXACTLY WHAT THEY MEAN....Don't assume!
Karen has it right. But don't be surprised if someone else using that term has a different definition. Another broker may think or use "turn key" to mean only that the property is newly painted and cleaned. Another term in real estate jargon is "puffiing" which is using advertising verbage to paint a picture that may not be entirely accurate. Karen and I would not do that but there are some that would.
Turn key usually refers to a home which includes furnishings plus bedding and towels, dishes, cookware, etc.... the things a homeowner would typically use on a daily basis. Essentially, the buyer can just "turn-the-key" in the front door, and move right in.
Turn key properties are especially appealing for second homes and rental properties, where the new owner does not intend to move furnishings and personal items from one home to another. For vacation properties, many new owners love the convenience of not having to worry about finding, purchasing and setting up a part-time residence. Turn key properties are ready to use and enjoy immediately.
Normally a "turn-key" property refers to the property virtually ready for you to just bring your furniture and move in. Landscaping, driveway, patio or deck, is all done. If it is brand new, many times all the appliances are in, carpeting, paint, etc.
It can be very appealing for people who don't have the time, or don't want to deal with making all the decisions on their own.
Good Luck in your search