Update: I had previously shared a workaround for embedding Facebook posts in your website but looks like you no longer need it as Facebook has officially launched the code generator for embedded posts at developers.facebook.com.
Just paste the URL of a Facebook post, hit the “Get Code” button and pick the HTML5 version of the embed code. Also, the warning on the Facebook page still says that “embedded Posts are currently available to a handful of news publishers” but it can be ignored as the generated embed code works just fine for any public post shared on Facebook.
You may see this sample webpage that uses Embedded Posts from Facebook though that profile hasn’t been approved for embedded posts yet.