I've read the guide about application data backup in Android here http://developer.android.com/guide/topics/data/backup.html, but I couldn't understand one thing - how cloud identify what user asks his information. The process is transparent for users, so they don't input any flags for recognitions. For example: user uses application, saves some strings information and then changes mobile device, downloads same application again, installs it and how he gets same information? Maybe there's something I've missed in that android guide?
The backup framework is independent of the actual backup service provider, and can use other backup service providers, but the default one is the Google Android Backup service (In the doc that you reference, The Basics contains a link to this page) which will back up the users' data to their Google accounts.