When posting a link to a website in Facebook (Google+ and the rest count too) you\'re given a thumbnail, or selection of thumbnails to choose from. These are tags from the
Yes, you can set a meta tag so that Facebook knows which image to pick.
See: https://developers.facebook.com/docs/opengraph/
Specifically, it is the og:image property, and it will tell Facebook's link share script to choose that image as its thumbnail.
Keep in mind though that Facebook does some caching, so if you've already shared the link once it may still be "stuck" on using the older image.
You can see whats Facebook getting out of your website by using the Facebook URL Linter. See: http://developers.facebook.com/tools/lint/ (The use of the URL Linter will also rebuild Facebook's cache)