A virtual debit card is a debit card that is issued (or usable) without a corresponding plastic card. The funds associated with the card can be accessed without use of a plastic card.
Virtual debit cards (and their cousins, virtual credit cards) are simply card numbers that are issued (without plastic cards) that can be used to conduct transactions. Some debit card issuers provide virtual debit card numbers instead of actual physical cards. The virtual card numbers can be used to purchase goods or services in the same way that a regular card can. Other debit card issuers provide virtual debit card numbers in addition to normal card numbers and allow you to use the virtual card number to make online transactions.