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I assume you're referring to paying points. A point is equal to one percent of the loan amount. You pay points upfront to get a lower interest rate. Over time, the point "pays for itself" in the form of lower interest payments.
Here's a purely hypothetical example. Let's say that you are getting a mortgage for $100,000. The interest rate is 5% if you don't pay any points. Your monthly payment for a 30 year loan would be $537 per month and you'd pay a little over $93,000 in interest over the life of the loan (assuming you hold it for the full 30 years).
You have the option of paying one point, which is equal to $1000 in added loan costs. This brings your interest rate down to 4.75%. Your monthly payment drops to $522 a month and you'd pay a little less than $88,000 in interest over the life of the loan.
A lot of people like to figure out the "break-even" point - the number of lower monthly payments that would be needed to recover the cost of the discount point. In the hypothetical example above, that would be $1000/$15 = 67 monthly payments, or about 5 years 7 months. So if you intend to stay in your home for at least this length of time, then buying down the interest rate would be a good long-term move. But the point would add to your initial closing costs.
Economic purists will note that this is not the entire picture - there's also the opportunity cost associated with paying the point. But I think you get the idea.