On the SEO tab of your Entry, scroll down to the heading: Facebook OpenGraph Image

Here you can upload an image that'll be used for display on Facebook posts that link to this entry.

Note: if you're using Craft 2, you'll need to click on on the Social tab (after you click SEO).

If you find that the image you have set is NOT displaying on Facebook with your link, the old image might be cached.

The first place you should start is the Facebook Debugger tool, make sure you are logged into Facebook or it won’t work. Enter the URL you are typing into Facebook that’s showing the incorrect image and click 'scrape again.'

If that fails, you will need to contact Facebook.