What it checks
Open Graph tags (the ones that start with og:) tell apps which title, description and image to show when your page is shared. A second set of card tags decides whether the image shows large or as a small thumbnail. This checker reads every one of them, plus your page title, meta description and canonical link, and grades each against what works reliably.
Fix means the preview is broken or missing something important. Improve means it works but could look better or load faster. Once it's all green, check the result in Link Preview.