The advantages of kitchen islands are many: Added counter space, added storage, and sometimes even an extra cook-top are just some of the positives. The added counter space is one of the main reasons people install them, but islands are manufactured or can be designed (if buying a permanent one) to fit almost any purpose.
The advantage of adding a permanent model is that it can be equipped with electricity, and often other convenience appliances such as a food prep sink or additional stove top. Most freestanding models are not equipped to handle this; but if the main purpose is to provide additional counter space or seating, freestanding islands are an inexpensive alternative to the high cost of having one permanently installed. Also, they have the advantage of being able to be moved around, allowing for more flexibility in room arrangement.