When you pay points on a mortgage, you're paying to offset interest. The payment is essentially a fee, and does not decrease principal.
In your example, if you pay $1,000 against a $100,000 mortgage, you're paying one point (one percent of the mortgage amount) and you're getting a .25% discount on interest as a result. You still owe $100,000 in principal. The advantage you're buying is a lower interest rate - which, if you plan to keep the house for a long time, can make a significant difference in the total interest you pay.
Essentially, paying points is a consumer betting that they will stay in the house for a long time (i.e. take a long time to pay the mortgage off).
This may be obvious, but a down payment is what it's called when you pay money upfront to decrease the principal. Both down payments and points will lower the total amount you pay back to the bank, but they work in very different ways. Down payments reduce the principal on the loan, while points reduce the interest paid. Which one is better for you will depend on how long you plan to keep the home, what your interest rate is, and other factors. Also, it's important to consider that mortgages are sometimes priced based on down payment size (i.e. the product you're offered at 5% down might have a different interest rate than the one you're offered at 20% down). And, a lower down payment often means that you'll be required to carry more PMI, which effectively raises your monthly payment. So - get the specifics on your deal, and check the numbers for each scenario, before deciding how to spend your money.