Touch ID is the name for the fingerprint reader in the new iPhone 5s. When you configure it, you have the possibility to register a number of fingers (5) with which you can unlock your iPhone.
Settings -> General -> Touch ID & Passcode -> Touch ID
For some reason this always failed after a couple of days on my phone. For some reason the fingers didn't 'register' properly, and I was forces to use the PIN.
The way to solve this (temporary) was to re-register the fingers, until I read about a way of training the device.
When you're in the menu where you normally register your fingerprints, you can register additional print data for each finger by just placing one og the already registered fingers on the home button. When the finger is recognized the registered finger entry on the iPhone turns grey for a second (as shown in the screenshot). Doing this for every finger a couple of times increases the registered data for those fingers. The more data that's registered the better the chance that the finger keeps getting recognized in the future.
UPDATE: With the iOS 7.1 update the Touch ID responds a lot better.