It reads the page's twitter:* meta tags (falling back to Open Graph tags the same way X itself does) and checks that a card type is set, that a title, description, and image are all available, and that the image is a full absolute URL rather than a relative path X can't resolve.
Add or fix the flagged tags directly in your page's <head>, then run the same URL through this tool again to confirm the fix landed and check the preview.