Well, unless you turn on synchronization you data are stored only locally, which means that if you loose that device you have also lost your passwords.
When you turn on synchronization the data are sent to the cloud encrypted so you can can recover them. To recover them from the cloud, you need to have authorized device or you have to use backup link from the email we have sent you when you have turned synchronization on first device.
The process of device authorization makes sure that no one else even in case he knows your avast account credentials can connect to your synchronization group.