Closing is essentially a meeting where the closing agent (the party who conducts settlement) takes money from the buyers, pays out money to the owner and makes sure that the purchaser's title is properly recorded in local records along with any mortgage liens.
All papers have been prepared by closing agents, title companies, lenders and lawyers. This paperwork reflects the sale agreement and allows all parties to the transaction to verify their interests. For instance, the buyer get the title to the property, lenders have their loans recorded in the public records and state governments collect their transfer taxes.
The closing agent reviews the sale agreement to determine what payments and credits the owner should receive and what amounts are due from the buyer. The closing agent also assures that certain transaction costs are paid (taxes and title searches).
Closing is also the time when "adjustments" will be made. For instance, suppose you've pre-paid taxes four months in advance. In this case, the closing agent will compensate you for the prepayment at closing by having the buyer pay you additional money.
It could also work in reverse. If you're behind on property taxes, the closing agent will reduce the money due to you at settlement by the amount of the unpaid taxes.