The scanner will not store images of your fingerprint on the iPhone; rather, data points are encrypted and stored within the iPhone's A7 processor. The phone then uses the digital signature to unlock itself or make iTunes purchases.
An Apple spokesman pointed to other security features the company has added to the phone. Apple customers who wish the use Touch ID also have to create a passcode as a backup. Only that passcode (not a finger) can unlock the phone if the phone is rebooted or hasn’t been unlocked for 48 hours. This feature is meant to block hackers from stalling for time as they try to find a way to circumvent the fingerprint scanner. Moreover, Apple says its Touch ID sensor is an improvement from the temperamental fingerprint scanners that often appear on consumer laptops.
Apple did note that its scanner is not perfect and may not work with moisture-laden fingers covered in sweat, lotion or other liquids. However, Touch ID is capable of 360-degree readability. Meaning, no matter which way you touch the Home button it will be able to read your fingerprint. You can also enroll multiple fingerprints so that the iPhone will recognize people you trust.
You can learn more from the video below or by watching Apple's introductory video.