A biweekly mortgage payment is a mortgage that collects payment every two weeks rather than once a month. The monthly payment would be broken up in half and paid every two weeks; it would not be a double payment.
The benefit of making a biweekly payment is that the interest is calculated differently and substantial savings can be made, decreasing a mortgage by several years due to the decreased amount of interest accrued.
The idea behind a biweekly mortgage payment is that it should decrease the interest that is accrued on the loan. Legally, there cannot be a double payment taken within any one-month period, so the only way that a biweekly mortgage payment is possible is if the payment is split in exactly half.