So glad you asked. The short answer is a vCard is a file containing contact information for a person or organization. It's been around for quite a while, and is supported by most address-book applications, e-mail clients, and many mobile devices. If you download a vCard and double click it, chances are good it will open up in your default address-book application and ask if you want to import a new contact (you do). Your address-book may even open as soon as you click the link.
If you'd like to know more about vCards in general Wikipedia has an article on them.