If you receive an automated email suggesting you update from Joomla 2.5.20 to Joomla 3.2.3 I suggest you do the following:
1. BACKUP your existing site using AkeebaBackup
2. Restore a backup in either a subdomain of your existing site or using WAMP or Xamp
4. You may find issues with your PHP version currently running or Plugins already installed that are not happy or compatible.
5. Better to be safe than sorry and save yourself a whole heap of time.