If you have an iPhone 5s or later, then the Home button has a built-in fingerprint sensor that can be used to unlock your iPhone or purchase apps and songs.
To control this, open Settings, then select Touch ID & Passcode. Enter your passcode and from here you can control if your fingerprint can be used to unlock your iPhone or purchase items from the iTunes & App stores.
Below this is the list of currently registered fingerprints. You can save up to five. To make a new one, tap Add a Fingerprint and go through the necessary process.
If you touch the Home button while looking at this list, the relevant entry will flash. To remove one, tap the entry then tap Delete Fingerprint. You can also tap the name and edit it if you wish to have something more descriptive.