Article in question: https://meta.stackexchange.com/help/flair
Flair is an image summarizing your accomplishments (your reputation, your badges, the top sites you've participated on), suitable for display on your own website or printing out and pinning to a vest if that's what you prefer.
That video link is private. Is this supposed to imply that somebody's vest is private? Remove it and replace it with this, which is the same video, but a live version (confirmed by Wayback Machine).