Why will reducing the boarding time reduce the costs?
It's not as much boarding as much as standing around does not generate any revenue.


Use Your Capital Assets: 25 minutes a day is a lot, and in some cases is equivalent to a domestic leg. Rather than arriving at 23:00, you could arrive at 22:30 and still squeeze in an additional short flight before midnight. If you're flying 10 flights a day and you can now fly 11, you're doing 10% more work with the same amount of assets. Estimates for a flight hour of a B737 are ≅ \$3000-\$3500 in the US, for an aircraft worth perhaps $60 million. 
Fixed Costs: You're looking at a bit of fixed costs, such as insurance. The more flying time you can squeeze out of the plane, the cheaper each hour will become on average.
Less Staff, More Product: You need a certain number of ground staff. If you can cut the time required for an aircraft to be handled by ground staff by 20% (50 → 40 minutes), that potentially means that they could handle an additional aircraft in their shift. This principle applies for airline flight crew, as well. It's a lot cheaper to let the your pilot fly a few hours more than needing to hire another one.
Standing around is not always cheap either: Depending on airport cost/fee structure, you may be charged less for the ground time. This is not only standing around; for instance, Munich airport charges you €44 for every 30 minutes of using a ground power unit.