Each point is one percent of the mortgage amount. The more points paid initially, the lower your interest rate will be. Sometimes it may not make sense to pay points, even though your monthly payment would then be higher. It takes about that time for the difference in monthly payments to offset the upfront costs of points. For tax purposes, points are considered pre-paid interest.
Points are deductible in the year they are paid if the mortgage is for a home purchase.
In the case of a refinance, these points must be amortized over the life of the loan. This is an insurance policy that protects the lender in the case of default on the loan. The cost of this insurance is added to the monthly mortgage payment. This is generally true even if the appraised value of the property is higher than the purchase price. PMI is not tax deductible.