Twitter has documented the metadata it looks for (similar to OpenGraph) to enable rich content sharing.
When someone tweets with a link to a page, Twitter scrapes the page looking for metadata that it uses to improve the presentation of that page. The data it looks for is similar to the OpenGraph metatags that Facebook uses, but Twitter has its own take on it. Apparently Twitter will fall back on Facebook OpenGraph metatags if their own metatags are not present.
Twitter's documentation is a good place to start.
Twitter's model is a "Card" .. and starts with a Card Type, which will be one of "summary", "photo", "gallery", "product", "app", or "player".
<meta name="twitter:card" content="summary">
There are specific metadata items you specify for specific card types.
Each card type corresponds with a presentation format used by Twitter. A photo card puts the picture more prominently, while a gallery card gives space for presenting multiple pictures, etc.
The
Twitter Card Validator helps you explore the format, and apply for approval with Twitter.
