"Closing" refers to the meeting where ownership of the property is legally transferred to the buyer. Your real estate agent will be present during the closing to help explain the process and forms to you and make sure everything goes as planned. By being present during the closing, he or she can mediate any last minute issues that may arise.
As the seller, you will need to be prepared to give over any necessary documentation regarding the property and, depending on the arrangements made during negotiations, you may be required to have done something specific in order to close.
Be sure to read all the documents and ask any questions you may have. It is important that you understand every document you are signing.