A billing address is the address where you are receiving the statements for your credit card. For your order to be approved when shopping online the billing address has to match this address since it is the registered address on the card.
In the USA, many online merchants require a US billing address. They do this to protect themselves against credit card fraud. The AVS (address verification software) credit card processors use helps them detect when credit card data is submitted incorrectly.
Not having a US billing address can be prevent you from placing orders on US websites from outside America. US Unlocked is a company that has solved this issue, by providing a US billing address to international online shoppers.