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:
https://developers.facebook.com/tools/debug
Jetpack automatically adds these Open Graph meta tags to your posts for you, unless you already use another Open Graph plugin.
Looking at your site, you seem to be using 2 other Open Graph plugins. Jetpack consequently has no control over the look of your posts on Facebook, and Facebook won't be able grab any information from the posts because of the duplicate tags.
I would suggest that you deactivate one of the 2 plugins (like 2-Click Social Media Buttons), to avoid any errors created by the duplicated tags.
I hope this helps.