Points are money you pay a mortgage lender at closing, and there are actually two kinds of points: discount points and origination fees.
Sometimes offered if you want to lower the interest rate on your loan. One point, in this case, equals 1% of the loan. Two points equal 2% of the loan, etc. You can usually go up to 4 points. One point typically lowers your interest by a .25%. If you plan to stay in your home a while, the amount you pay for discount points could save you money in the long-term by reducing your monthly mortgage payment.
Are fees charged to you by the lender. Either negotiate these fees with your current lender, or shop around when choosing a lender to see what the origination points they charge are.