A QR Code is a two dimensional barcode. You are probably familiar with barcodes at the store (UPC's) and on books (ISBN's), these are one dimensional barcodes, information is only encoded one way, left to right. A two dimensional barcode includes information both left to right and top to bottom. You may have seen these on UPS or FedEx packages. QR codes are freely usable and have (along with some other 2D barcode formats) been picking up a lot of traction in Asian and European markets, particularly when combined with cell phones. Typically a QR Code will include a small piece of information useful to a mobile user (phone numbers, email addresses, website addresses, or in our case here a vCard).
If you'd like to know more about QR Codes and some of their uses, Brian Suda has written up a nice article on the Opera Developer website.