Like nearly all merchants, we use an Authorization / Charge method of charging a credit / debit card. This means that when you click on "Place Order" on our site, the credit card you supply is immediately electronically queried, or "Authorized" for the amount of funds on the order. On your own credit card website, you'll usually see this as the "Temporary Authorizations" tab or something. Not actual charges, just placeholders in their buffer until the actual charges show up. If the transaction is canceled prior to shipment, the authorization will fall away unused and generally un-noticed. Once your order goes further into processing by us however, we tell our credit card processor to replace the authorization with an actual charge for the amount. Your credit card then places the actual charge against your account and deletes the authorization from the buffer. (Note the two separate transactions, places the charge and deletes the authorization, in that order. This is intentional)
If you use a debit card tied to a checking account however, there's no "buffer" to hold the original authorization except your own checking account. (Checking accounts weren't taken into consideration when credit card charging rules were written, and they generally don't have "buffers") So the authorization may show as an actual debit against your checking account at first.
Further, when the authorization is to be replaced with the actual charge later, since they are two separate transactions, your bank will place the charge first and then come back and remove the authorization, just like a credit card. On a checking account however, this means that they first will place the charge against your checking account, and for a brief time you will have two debits against your checking account. until they then remove the authorization. Sometimes this is somewhat less than immediate. Simply put, yes, we accept debit cards, but we certainly don't encourage them.