Many lenders set up an escrow account for the buyers at closing. This is an account used at a later date to pay for items for which the buyers are responsible. When the buyers make their monthly payment, they pay principal, interest, taxes, homeowner insurance, and private mortgage insurance (PITI), if applicable.
An escrow account provides buyers 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 the buyer would not have enough funds when bills come due.
At closing, you will be charged with taxes from the first of the year until the day of closing. These funds are placed in the buyers' escrow account. The buyers will also prepay several months of taxes. Then, on the first of every month when the buyers make their payment, they will deposit a month's worth of taxes into their escrow account. Thus, when the tax bill is due, your tax contribution, the buyers' prepaid tax plus the buyers' 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 the buyers pay the yearly premium. The next premium will be due on the one year anniversary. Thus, when the buyers make their monthly payment, they 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.