Essentially a wrapper for your regular credit card or debit card account, a virtual card number is good for one use only. When you use the virtual number, the bank that supplied it charges your purchase to your regular credit or debit card, but hackers never gain access to the underlying credit card information.
Various financial institutions maintain some sort of virtual credit card program. Bank of America, for instance, offers a ShopSafe service, and Discover has a similar service. Check with your bank or card issuer to see what options are available. Alternatively, consider Shop Shield, a virtual card number service that you can use with any credit card or checking account.