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, ...).
You can see what Facebook sees by entering one of your posts' URLs in Facebook Debugger:
Jetpack automatically adds such Open Graph meta tags, except if you use another plugin to handle these.
Looking at your site, it seems that you do indeed use another plugin, as the Jetpack Open Graph meta tags are not displayed. However, that plugin must not be configured properly, as it doesn't add the tags to your posts at the moment.
Check your list of active plugins and you should find one of the following plugins:
Official Facebook plugin
WordPress SEO by Yoast
Add Link to Facebook
Facebook AWD All in one
Header and Footer
NextGEN Facebook OG
SEO Facebook Comments
Simple Facebook Connect
Social Sharing Toolkit
WP Facebook Open Graph protocol
One of them can be configured to add Open graph meta tags to your posts.
Let me know if it helps.