What in the world is Internet self-regulation?

A few months ago, Singapore Minister Lui Tuck Yew commented that the Internet community in Singapore missed the chance to show that it could shoulder a higher degree of self-regulation by not rebutting many of the online attacks on Member of Parliament Seng Han Thong who was physically attacked.

To be fair, everyone has been throwing about the term "self-regulation" long enough but we are not quite sure what kind of creature this is. This got me thinking: What does this self-regulation look like? Is this a panel of some kind or are there appointed moderators? Who becomes "god"?

Is this "regulator" responsible for all regulation? When it fails to regulate or regulates wrongly, do we fire it? If we do, who then steps in? the government? If so, which government?

What if someone fails to accept the authority of the regulator?

What kind of power can this regulator have (for example, no postings from violators for one day, banishment from the Internet etc.)?

I would like to hear ideas from you.