Edit: After half day, my wife’s Mac started having the same problem. I have then applied the solution that I found in the Apple
Apple's New Fingerprint Reader With Touch ID On The iPhone 5S
So the rumors were correct, a fingerprint reader will be found on the home button of the latest iPhone 5S.
You can simply hover your finger over the home button and it will detect your fingerprint. The details of your fingerprint are claimed to be stored locally, however, Apple did not go into too much detail about this; they simple quoted that the data would ‘not be stored on Apple Servers’.
We can expect to see Touch ID opening doors to developers to allow implementation into banking and shopping apps, but this will need to be carefully controlled. Apple currently offer the fingerprint unlock for purchases in iTunes App Store, and the iBooks Store as well as unlocking your device using it.
Finally, Touch ID can store multiple fingerprints giving multiple people access to your device. This will evidently lead to your kids buying apps or family members reading your texts. Furthermore, it can read a finger print at any orientation, useful I guess if you ever want to use your phone upside-down.
This animation shows how Apple managed to neatly pack all the gadgets inside there: