Answer:
The service sector grows because of the same reason that any other economy sector grows: the demand for it increases.
Step-by-step explanation:
Demand increases because new services are created, or existing ones obtain more customers: a larger market share.
In the case of Amazon, the service it offers is deliveries, but Amazon took deliveries to its logical conclusion, becoming an online store that essentially sells everything, from books to car accessories, to fruits and vegetables.
Amazon has become a giant company because it exploited a existing market that had a lot of untapped potential, and customers at the same time responded by demanding even more of these services. In other words, Amazon and the customers formed a virtous cycle that feeds economic growth.