It works by calculating and including a bonus amount that you receive when you buy 2 or more rides.
In New York City, a subway or bus ride costs $2.75. When you receive the 11% bonus, it is added to your card after the cost of your fares. If you do not use your bonus, the NYC Transit keeps it, and you lose it.
Subway Saver stops this by calculating the amount you pay for your rides with the bonus being included into the cost. This way you save money by purchasing only what you need.