The Anthropic Principle, in its weak form, is a response to the realization that the parameters that comprise the Laws of Physics have to be very, very unique in order for something as complex as a star to form, much less something as complex as a human being. By “very, very unique” we are talking something in the order of 120 magnitudes of uniqueness. (To put this into perspective, the number of atoms in the whole universe is estimated to be a few less than 80 magnitudes.)
The fundamental parameters are things like the masses of the various fundamental particles and the strength of the fundamental forces -- for instance the mass and charge of the electron and the strength of gravity. Physicists used to assume that a final theory of nature would explain why each parameter had the value it has, but it increasingly appears that there is no necessity for these values. It appears that they could take on any value along a continuum of values (indeed it is contingent that they exist with any value at all). So the question arises: Why do they exist and why do they have the values they have?
The Anthropic Principle provides a very simple answer to this question: we are here, therefore the parameters provided the right conditions for us to be here; we should not be surprised that the parameters are those that allow us to exist, whatever the odds against them. An analogy might be that if we win the national lottery, we might be surprised to do so, but we should not be surprised that somebody wins it.
As far as it goes, this “explanation” is true, but it doesn’t actually explain much. A proper scientific explanation would provide a mechanism by which these parameters become determined, and the Anthropic Principle does not even attempt to provide such a mechanism. (In my experience, the only attempt to answer the question of the parameters that provides a mechanism and is falsifiable is the theory of Cosmological Natural Selection developed by Lee Smolin.) The analogy with the lottery is not really apt, either, because there is no good reason why there has to be a winner in the cosmic lottery, unless we assume an infinite number of universes, each capable of having a different set up parameters. It has become fashionable to assume this, but I don’t think many people think through the consequences of this assumption – indeed I feel rather certain that no human being is capable of thinking through the consequences of this assumption.
The Anthropic Principle, in its weak form, seems to me like an intellectual curtain. Behind the curtain is the huge mystery of our being here. But for those who temperamentally dislike mystery or anything that the human mind is powerless to penetrate, the Anthropic Principle conveniently hides the mystery from view. If like me, you love a good mystery, than you also would prefer to throw open the curtain and contemplate the great darkness beyond. Somewhere in that darkness, after all, is the reason we are here.