While some were wowed by the fingerprint scanning Touch ID home button on the iPhone 5s (http://www.gsmarena.com/apple_iphone_5s-5685.php) others have a tough time feeling safe that Apple won't "accidentally" share their fingerprints with someone not meant to have access to them.
So an Apple spokesman stepped in an said that the iPhone 5s won't store fingerprint images on the device but instead will encrypt the fingerprint data on the phone's A7 SoC.
(http://cdn.gsmarena.com/vv/newsimg/13/09/apple-talks-touch-id-security/gsmarena_001.jpg)
Even if someone did hack into your device and managed to get inside the A7 chip they likely won't be able to extract the fingerprint information out of it.
Furthermore, Apple requires every fingerprint to be created with an accompanying passcode, which in a scenario when the phone has been rebooted or hasn't been unlocked for 48 hours will be required instead of the fingerprint, which is a nice two-step security verification.
Source (http://blogs.wsj.com/digits/2013/09/11/apple-new-iphone-not-storing-fingerprints-doesnt-like-sweat/) | Via (http://www.theverge.com/2013/9/11/4720218/apple-clarifies-touch-id-storage-details-to-calm-potential-security-fears)
GSMArena.com