When you share a post on Facebook, or when Jetpack Publicize publishes a post to your Facebook page, Facebook crawls the page and looks for Open Graph meta tags in the head to build a complete post preview (with an image, title, description, …).
Jetpack automatically creates these Open Graph Meta tags for you unless you already use another Open Graph plugin, in which case we let the other plugin handle things.
You can see what Facebook sees by entering one of your posts’ URLs in Facebook Debugger:
https://developers.facebook.com/tools/debug
If you’re not happy with what Facebook sees, I’d suggest checking what plugin generates the Open Graph Meta Tags on your site, and if it’s not Jetpack, make sure your Open Graph plugin is configured properly.
Let me know if it helps. If you continue to experience issues, do not hesitate to post your site URL here, so I can have a look!
If you want it to remain private, you can also contact us via this contact form:
https://jetpack.me/contact-support/