Private mortgage insurance or "PMI" policies are designed to reimburse a mortgage lender up to a certain amount if you default on your loan and your house isn't worth enough to entirely repay the lender through a foreclosure sale. Most lenders require PMI on loans where the borrower makes a down payment of less than 20%.
Premiums are usually paid monthly and typically cost around one half of 1% of the mortgage loan. You can normally cancel the PMI once your equity in the house reaches 20-25%, so long as you've made timely mortgage payments. For more information, see Nolo's article Getting Rid of PMI (Private Mortgage Insurance)