Facebook asks publishers to insert og:image tag into HTML. This tag specifies a main article image, the one that should be displayed on Facebook when the same article is shared/posted.
Sometimes Facebook doesn’t display the image, although it is specified in HTML via og:image. The most probable reason is “Facebook caching”. FB cached given URL at a time when it had no image. The solution to this problem is here.
Go to the link above, insert article URL and click Debug. If the tool shows image in post preview, then FB will probably display this image when an article is shared.
If article HTML doesn’t contain og:image tag FB will try to figure out which image to use on its own.