Apple acquired AuthenTec back in 2012, and a lot of rumours circulated about the possibility of iPhones using fingerprint sensors created by this company. Come 2013, this has come true in the form of an integrated fingerprint sensor called Touch ID on the home button of iPhone 5S. In the process, the iconic rounded square marking in the button was sacrificed in the name of progress. The physical button is still clickable as always. The sensor works only when you leave your finger on the button without clicking.
Many experts view biometric authentication such as fingerprint scanning as a good way to "augment" security. It is by no means a complete replacement for existing measures because you can't change your biometric characteristics, and the detection can be fooled with sufficient resources and will. So it's generally recommended that this is used in conjuction with another authentication method such as ID & password. That said, Apple has decided that it's good enough to be used as an alternate method of entering passcode for unlocking lock screens.
This doesn't sound good from strict security standpoint because the biometrics are used to "replace" rather than "augment". However, Apple's rationale is that a large number of people don't even set passcodes, and by providing this alternative in a convenient package, phones would be somewhat secure, than not secure at all. Then, the convenience angle must be sufficiently strong to gain traction.
Using this feature for some time, I can say that this would indeed be the case. Read on to see my demonstration.