A transient license is a city occupational license that allows you to rent property by the day or by the week. This is a very popular way to achieve rental income on your investment property or second home.
These licenses are very valuable. In most cases, the City of Key West is not issuing new licenses so you must purchase a property that has a current one. In some limited cases you can "buy a transient license" from one property and transfer it to another. This is a complicated process and you should consult a local real estate attorney to assure the feasibility of this transfer.
Most properties in Key West can be rented monthly. That is called a "non-transient rental license". This is also an attractive venue for achieving rental income without the wear and tear of weekly or daily rentals.
You should be aware that different communities and condominiums may have additional rules regarding these rentals. Make sure your realtor provides this information for you prior to signing a contract for purchase.