Your application can store state in two places: the SD card; and the application's own private storage.
The SD card is completely public and everyone can access (and modify) the files there.
Your application's private data directory is supposed to be secure, in that only your application (and other apps that your application trusts) can access it, but in practice if the phone's been rooted it's trivial to copy files out of it.
See the openFile*() and openOrCreateDatabase() methods in the documentation for Context for access to your private data directory.