According to Twitter, a Website Card is a powerful ad format that allows users to preview an image, related context, and a clear call to action in their timeline.
Include conversion tracking in your campaign to measure actions that happen off Twitter, such as a sign-up or purchase. Use a Website Card to grow your site traffic.
So that definition is about as clear as mud to most of us. WebCards have been around and evolving since at least 2007 in several forms. The latest is the Website Card, the brainchild of Twitter.