Many lenders will set up an optional escrow account for you at closing. This is an account used at a later date to pay for items for which you are responsible. When you make your monthly payment, you pay principal, interest, taxes, homeowner insurance, and private mortgage insurance, (PITI) if applicable.
An escrow account provides you a way to set aside monthly funds that will be due later in the year. Property taxes are due annually toward year end. Escrow accounts limit the lender's risk that you would not have enough funds when bills come due.
At closing, sellers will be charged with taxes from the first of the year until the day of closing. These funds are placed in your escrow account. You will also prepay several months of taxes. Then, on the first of every month when you make your payment, you will deposit a month's worth of taxes into your escrow account. Thus, when the tax bill is due, the sellers' tax contribution, your prepaid tax plus your monthly tax contribution will add up to 12 months worth of taxes. This should be enough to pay the tax bill.
Homeowner's insurance is also deposited in the same escrow account. At closing you pay the yearly premium. The next premium will be due on the one year anniversary. Thus, when you make your monthly payment, you are contributing one month's worth of property insurance. When the premium is due in a year, there will be enough funds in the escrow account to pay the bill. Mortgage insurance is handled in a similar manner.
If you sell your home, you will owe taxes and insurance through the day you close. Excess funds in the escrow account will be refunded to you.