As they sound, private airport transfers are just that - an exclusive door to door service that makes your life easier on arrival at the airport. Usually we are talking up to 8 max for a private airport transfer - taxis take up to 4 and then it's luxury minibus/mpv transport.
Your driver will meet you once you clear international arrivals and will sort all your luggage and skis into the vehicle for transfer. You will be taken to the door of your accommodation - ready to face anything! The only difference with a larger group - is that you use a luxury MPV or minibus.
Definitely the easy way to start your holiday, advantages include one to one service and more space. You can also take the transfer at your own pace - in the knowlegde there's only you and a few friends to worry about.