A "Fingerprint," like on a person's hand, is used to identify a person via something very small or obscure. In computers, it is used as unique identifiers to determine if a certificate or PGP key has been tampered with via a string of unique characters. A different Fingerprint results if the contents of the certificate or key change in any way. This is accomplished using a hash function. Many people list their PGP fingerprint at the bottom of their e-mails to protect against someone else interfering with the use of their key, also known as a Man-In-The-Middle Attack. This is much easier than searching the entire block of text for differences.
The fingerprint itself often looks like a series of numbers and letters A through F that certificates and public/private.
A PGP key fingerprint looks like this:
DFF3 30DD A34F 7F4A 88FF 934F 98B1 AFE2 3218 A4FA
Most browser/S/MIME fingerprints: