Khoi Vinh has a great introduction to software cards for presentation and rich content:
Even as the notion of cards as the next big software interaction paradigm continues to gain momentum, it hasn’t gotten much easier to explain to the uninitiated what, exactly, a card is. When asked this question, I find it hard not to ramble on at great length, and even harder to avoid using technical jargon, which usually produces diminishing returns in conversations with “normal people.”
Make sure to check out his Pinterest board for screenshots of card UIs and see what they actually look like.
While I don't rely on many card-based apps or web services, I do believe that Twitter cards are largely underrated and ignored by people who use third-party Twitter clients, which can't display cards.
In my limited experience, setting up a MailChimp card for our MacStories Weekly newsletter doubled our number of subscribers thanks to its design and ease of use. With Twitter Cards, the link I shared appeared as a card inside Twitter timelines with an interactive signup form to subscribe with one click.
That's a powerful idea, potentially applicable to hundreds of web services and publishers that are sharing content on Twitter. I'm definitely planning to explore cards more for MacStories.