Both posts and web pages can be setup to define your OG:Image and OG:Description (this is what Facebook uses when shared). The Post or page title represents the OG:Title.
With both pages and posts, any time you add or edit the title, image, or description you should update Facebook using the description below.
Changing Advanced Settings after publishing
You can update these after the fact however you may notice posts shared to Facebook don't reflect the changes because Facebook uses "caching" to improve performance.
You can clear the cache by visiting https://developers.facebook.com/tools/debug/ and pasting the URL of the content you want to update in their tools.
Steps to clear Facebook cache:
Copy & Paste the URL into the text box
When the page reloads click "Fetch new scrape information" button.