MSDN Magazine cool article about Windows Store App (aka Modern App, aka Metro Style app) lifecycle.
The author, Rachel Appel, raise the veil from how an app is managed by the OS in Windows 8.
Actually there are few states for an application to be in and few transitions but the devil is in the details!
For instance, your app may get terminated without the user closing it. This would be done after the OS suspend it but when your app is launched again, it would need to behave as if it got back from the suspended state and recover all its runtime state from durable storage. That easier said than done and this is where the app designer has a major role to play!