A credit card is a payment method that allows the cardholder (the person whose name is on the card) the ability to pay for goods and services at merchants now, and then reimburse the issuing entity at a later date. The cardholder is issued a line of credit when first receiving the card, and may not exceed this amount in goods they purchase without paying down the balance.
With most credit card companies, your balance will accrue interest if not paid in full every month (this is not the minimum payment, but the entire balance). These interest rates can range from as low as 9% to as high as 30%, and is typically dependent on your credit rating. In addition, you could be liable for penalty fees and acquire a negative history on your credit report if the minimum balance is not paid in a timely fashion each month.
The two biggest credit card companies are Visa and MasterCard. Many people also assume that American Express is also a credit card company, but this is in fact a charge card, which differs from credit cards in that a balance may not be carried over from month to month, but must be paid in full each payment cycle. The biggest difference between the two is that credit cards usually involve a third party that pays the merchant immediately, while charge cards include a deferred payment which the merchant agrees to accept, with the knowledge that the charge card issuer will pay the balance if the cardholder does not.