Facebook looks at the meta="description" element of the shared link to determine its excerpt. The following link discusses how to do this:
Matthew Ebel » Blog Archive » Adding WP Post Excerpts to Facebook Links
The process requires modifying the header of your current theme, usually the header.php.
It’s also possible that the meta="description" element is missing in your theme (like in CRC‘s Suffusion theme). If that’s the case, just add the missing element.
[EDIT: Ditched this and went with All in One SEO Pack plugin instead.]
