"Torturing children for fun is wrong" seems to be a reasonable sort of thing to say, whereas "playing Wii Golf is wrong" seems to a massively unreasonable sort of thing to say.
An obvious way to gloss the distinction is to say that "torturing children for fun is wrong" is clearly true, whereas "playing video games is wrong" is clearly false. Sadly, however, the world fails to contain the sorts of metaphysical facts that would make "torturing children for sport is wrong" true. After all, the statement seems to be an attribution of a certain property (wrongness) to an action "torturing children for sport" and no such property seems to exist. At the very least, there is no evidence for the existence of such properties. Depending on one's theory of evidence, this might be enough--such properties don't constitute part of our best overall theory of the world, so it's rational to actively disbelieve that there are any such things--but even if one's epistemic stance leads one to agnosticism in cases where there is no evidence one way or the other, this doesn't help much in terms of making sense of the difference in our atittudes towards "torturing children for fun is wrong" and "playing Wii Golf is wrong."
That distinction surely has to do with our moral intuitions, and for shaved apes like us to "have moral intuitions" is surely ultimately for us to have a certain sort of neurological event, one resulting from genetics, environment or some eccentric combination of the two. If moral properties exist, and they are non-physical (as they certainly seem like they would be), no remotely plausible causal story relates them to humans having moral intuitions about them.
At this point, of course, one may go in any number of directions. For example, one can try to make sense of moral properties so they aren't non-physical. Volumes can be (and have been) written about this proposal in all of its myriad flavors--synthetic reductionisms, sentimentality theories and so on--but for the moment I'll just say that, while I've argued for this kind of approach in the recent past, at the moment I find the prospects for this sort of project fairly bleak.
On the opposite extreme, one can simply bite the bullet and say that, the world lacking the right sorts of facts, "torturing children for fun" and "playing Wii Golf is wrong" are equally false, to the same extent and for the same reason, and deny that our inclination towards the first statement and against the second tracks anything interesting. The case for this is easy enough to make, but one might think that if we can find a way to do better, we should.
The most familiar way to make sense of joining the full-fledged moral realist in endorsing some moral claims but not others, while joining the full-fledged error theorist in denying that the world contains the right sorts of facts which would make moral claims (at least moral claims interpreted literally as exactly the sorts of things they seem on their face to be, which is to say as descriptive claims attributing certain non-physical properties to human actions) true, is Gibbard/Blackburn-style "quasi-realism." Minimalism about truth, understood not in the straightforward "Truth As Disquotation" way in which truth is still taken to only apply to ordinary descriptive statements--"'snow is white' is true" means nothing above and beyond "snow is white"--but in terms of talk of "assertion condiitons," is supposed to connect these seemingly incompatible dots.
The quasi-realist, however, faces all sorts of obvious problems, from difficulties about how to make sense of the technical logical details(the Frege-Geach Problem) to the fact that it seems to entail relativism about truth to the poorly-defined and implausible nature of the very idea of "assertion conditions."
So, if one thinks these are big problems, but shares the quasi-realist's core committments--(1) some moral claims should be endorsed, others rejected, even though (2) there are no moral facts--what's to be done?
In an interesting article back in 2005 in the Australian Journal of Philosophy, Daniel Nolan, Greg Restall and Caroline West propose a version of fictionalism about morality that they take to successful avoid the vices of quasi-realism while assimilating all of its virtues. I'll have more to say about my own position on all of this, and a more detailed discussion of Nolan/Restall/West, soon, but for the moment I'll just settle for saying that the article is worth reading.
[Update: If you're reading this at a place where you can't access the published version for free, Greg Restall points out in the comment thread that an earlier, longer version is freely available here.]