Only Apple's official apps (App Store, iTunes, etc.) could make use of the iPhone 5S's fingerprint-scanning technology. Now, for the first time, third-party apps (like Mint or Facebook) can use Touch ID to log in, instead of typing a password.
The app does not store your personal fingerprint data. Rather, your fingerprint will unlock a username and password stored in your phone, like Keychain. So your unique fingerprint is never accessed by other apps. It stays safe in your iPhone 5S.