"Under contract" mean that two willing individuals, a buyer and a seller have agreed to transfer real property. This is not the "official sale." The sale is considered offcial (final) once it "closes." Once closed the new owner takes possession of the property for his/her personal use.
Under contract in a nutshell means that there has been a meeting of the minds between the Buyer and the Seller--in other words they have come to an agreement under the terms which the property will be transferred to the Buyer. However, no sale is official until the transaction closes--which means it has been officially recorder in the public records.