If you flag a post, a notice in red appears on it indicating that it received a flag. Everybody can see this notice, but they cannot see who submitted it.
When a post is flagged, it gets added to a separate moderation queue that only staff members can access. From there, we can either remove the flag/s or take down the post. If necessary, we could also navigate directly to the page, if the post could be fixed by making an edit. This is what it looks like.
Multiple users can flag one post. If a post receives a fifth flag, then the site will automatically remove the post, without intervention from any mod or editor. You can tell when flagging a post will end up removing it, as the button will say 'flag and hide' instead.
Receiving or giving out a flag comes at no consequence to anybody. It's just a way of alerting someone with some mod powers that there's potentially a problem with a post. It is always appreciated as it can help us resolve problems faster.