If, like most people, you owe money to the credit card company, the outstanding debt is a debit balance for you, but a credit balance from the credit card company's perspective. When you spend money using your credit card, the amount is debited from your account and credited to the merchant's account.
The terms "debit" and "credit" originate from accounting entries made to record financial transactions. Every time a financial event occurs, whether it is a sale, a new investment in a corporation or the acquisition of new equipment, two entries are made. One side of the balance sheet is debited, while the other is credited. As a result, the left and right sides, comprised of "assets" and "liabilities plus shareholder equity" respectively, are always equal in aggregate. This system is referred to as "double-entry accounting".
To have a debit on an account, means that you owe money. Since most credit card holders owe money to the credit card issuer most of the time, the normal state of affairs is for the consumer to have a debit equal to her outstanding balance. Keep in mind that credit card issuers make money by charging interest. Therefore, your total balance equals all credit card purchases plus interest charges added to your account -- both purchases you make and the interest accrued on your account are debited to your account.
It is not impossible, however, to have a credit balance. If you pay your outstanding balance in full every month and suddenly discover an erroneous past charge, you may receive a credit equal to that amount. In other words, the money that was mistakenly added to your total outstanding debt may be returned to you. Consequently, your credit card balance may have a net credit. If for instance you had a zero net balance when a mistaken past charge was discovered and $100 was returned to you, your balance will be a $100 credit. If you were then to make a credit card purchase for $250, the net balance after this transaction is a debit of $150.
From the bank's perspective, your outstanding credit card balance is a credit. This is because what you owe, is an asset from the bank's perspective. Every time you make a purchase, the bank debits your account and credits its own receivables, thus keeping both sides of its balance sheet equal. Note, however, that the bank does not expect its customers to pay of all balances eventually. It knows all too well that some people will default and therefore periodical adjustments are made to reflect this inevitable reduction in credits.