By way of clarification, Starwood is a hotel company and Starpoints can be redeemed for award stays at their hotels brands including Westin and Sheraton. In this context, however, the idea is that you would accumulate Starpoints and transfer them to an airline frequent flyer program because most airline programs allow open-jaw redemptions.

Other hotel chains offer airline transfers, but Starwood offers the most favorable exchange rate. 20,000 Starpoints = 25,000 airline miles (on most carriers, notable exceptions are Continental Airlines and United Airlines.) While it is not necessary to stay at Starwood hotels to use the program you would accumulate points faster if you did.