Twitter Cards are special layouts for media that appear when a web page is linked on Twitter. All of Koken's default themes include Twitter Card metadata that create cards like the following, which was created by linking to an album page:
At the time of this writing, Twitter is testing the Cards feature, so in order for Cards to appear in tweets linking to your site you have to submit your site for approval. Twitter should eventually be lifting this requirement and start allowing any web page with the appropriate metadata to function, but for now your site has to be on their list.
If while validating your site at Twitter you receive an "Invalid card type" error your Twitter username in Koken is likely empty. To edit, click Settings at the top of the console, then "Administrator" in the left column. Enter your Twitter username (without "@"), save, and try validating your site again.
Twitter's gallery card is used for album pages and requires at least four images in the album in order to validate. The card will still work, it just won't validate, so if you see an error concerning images not being found that's likely the reason.