The first digit signifies the system that the card runs on:
3 - Travel/entertainment card (ie: American Express/Diners club)
4 - Visa
5 - Mastercard
6 - Discover Card

The actual card number also varies by the system. (For example, American Express cards start with 37, Diners club cards start with 38)

Visa: Numbers two through 6 are the bank number. Numbers seven through twelve or fifteen is the account number. Finally digit 13 or 16 (the final number) is a check digit.

Mastercard: Numbers two and three, two through four, two through five, or two through six are the bank number (This depends on if digit two is a one,two, or three.) The numbers after the bank number up through fifteen are the account number, and the final number is a check number.

American Express: Numbers three and four are type and currency. Numbers five through eleven are the account number. Numbers twelve through fourteen are the card number within the account and the last number is a check number.

Hopefully this will give you a better understanding of what you are looking at the next time you pull out the plastic! So what about the back?

The back of the card has what is called a magnetic stripe. (Commonly called a magstripe.) It is made up iron magnetic particles in a plastic film. If a credit card terminal ever refuses to take your card it is most likely because this stripe is dirty or scratched. The stripe can also be erased by exposure to a magnet. (This can even happen with a basic refrigerator magent.) This stripe has all information associated with your account. This is why a merchant pays less for a card swipe when compared to a key entry.