In more detail
Points (also called discount points) are prepaid interest: you pay more at closing in exchange for a lower rate for the life of the loan. How much one point lowers the rate varies by lender and market, often around 0.25 percentage point. Because they are a cost of borrowing, points are included in the loan's APR. Some lenders offer the reverse, "lender credits", which pay part of your closing costs in exchange for a higher rate. Origination fees are sometimes also expressed in points but do not lower the rate.
Why it matters
Points pay off only if you keep the loan longer than the break-even period. If you are likely to sell or refinance within a few years, the upfront cash is usually better kept, or used as a larger down payment.
Example
On a $300,000, 30-year loan, one point costs $3,000. If it cuts the rate from 6.5% to 6.25%, the payment falls from $1,896.20 to $1,847.15, a saving of $49.05 a month. Break-even: 3,000 / 49.05 = 61.2 months, about 5 years. Kept for the full 30 years, the saving totals $17,658.90.