An example would be an eBook reader. You are reading a book on your laptop and the application knows what page you were last reading. (That happens already with a single computer.) On the train to work you open that application on your phone or tablet. It opens at the page you were last reading on your laptop.
Or, you have a favourite game that you play on several devices; the high score is the same on all of them. I'm sure you can think of other examples where maintaining the state of an application is useful.
A real-life example is that I installed a trial of Windows 8 in a VM on my desktop and set up the mail application with four email accounts. When I installed the retail version on my laptop I opened the mail app ready to go throught the setup again, only to find that it was already configured. I just needed to confirm the passwords for the accounts (probably a good idea). Nice!



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