It won't take a math genius to see that adding extra to the amount paid to the lender every month cuts down considerably on the principal. How many payments do you need to make exactly in order to bring down your mortgage?
Thankfully, it's not a large amount. However, not all of that will go towards the principal. It's because of the way the mortgage is made up:
The bulk of the mortgage is the principal, the actual amount of money that you'd borrowed which shows up on your papers. Then, you have the interest. This is an amount that is predetermined which the lender is allowed to charge you for the use of their money. Then, you have an escrow fund for any taxes that must be paid on the real estate and the homeowners insurance in case of default or unforeseen incidents.
Whether you make extra payments or tack on more than you're supposed to pay every month, it will lessen your debt dramatically. Once you pay more, the excess goes to paying off your principal, which in turn lowers your interest. So, you will be saving on interest payments since these are always computed based on the principal amount.
You can dictate where the money will go. The usual excess payments get credited to the principal but you must specify that they do so. Some lenders do this automatically but it's always best to be sure. The money can also be put in the escrow fund. While it won't lessen the principal, it will cut back on the amount you will need to pay monthly since you'll have more money with which to pay taxes and insurance.
The danger of not specifying where your extra payments will go is that they may just be put down as an advance payment. For example, if you send in two checks, both with the amount needed for the monthly payment, the lender may very well assume that you made a payment for two months instead of using one to pay off the principal.