A mortgage point is a fee that is calculated as 1% of the loan amount. A mortgage lender can charge one and more points. There 2 types of points: origination and discount points.
Origination points are charged by your lender for covering loan related costs. This fee can be deductible only in one case, if it is used for obtaining a mortgage, but not for covering other closing costs.
Discount points are prepaid interest on a mortgage. You can lower your interest rate paying more points in the beginning. You can cover up to 4 points depending on your financial possibilities. These points are tax-deductible.
Choosing to pay points or not depends on your monetary situation and plans for the future. If you can make higher payment now, you will benefit with the interest rate during your repayment period. But if you want to lower your closing costs, you should better choose to pay zero points.
Find some more information to consider before home buying here:
How much money to borrow when choosing a mortgage?