MyBB Community Forums

How can I set the thumbnail image for my forum, so whenever I link the URL of my forum for example on facebook, I would have thumbnail shown?

That would require your site being compatible, check it at http://developers.facebook.com/tools/debug
You also need to add the following into the head of your sites home page

<meta property="og:image" content="[url to image]" />
<meta property="og:title" content="[page name]" />
<meta property="og:description" content="[content description]" />

It is also recommended that you register a Facebook App ID for your site, otherwise the debugger will return errors.

Or you can use plugin for that - SEO Titles