The reason why upgrade is necessary is that every few months, a new version of Drupal is released. We upgrade the latest version in order to fix security issues and take advantage of many new features. After the process we check whether the contributed modules we rely on have been upgraded or not because the old versions of modules do not run on an upgraded version of Drupal. (e.g 4.7 modules do not work on a Drupal 5.x site).
When the upgrading process is going on we take care that all your database and the existing site has a backup, followed by that we download and unzip the new Drupal files to the server and late on run the update.php script, which updates your database.