It means that anything this user says has to be 'vouched for' by someone more popular in the community before it can be seen by all accounts. It's a button next to the "X minutes ago" field on a post that allows users like me to signal "this one's okay to be seen". You should have this ability already, as your account fits the requirements for it.
The "vouch" menu option only appears when you drill down on the timestamp of a dead comment. Which means you need to set the "showdead" setting on your HN profile to "yes", otherwise you won't see the comment in the first place.
