I think the theist belief is that God existed before Creation, so He existed independently of other things - i.e. absolutely. The absolutes claimed by theists are attributes of a Creator God as opposed to things defined relative to God.
Relative morality is the belief that what is moral for you might not be moral for me - morality is only a matter of personal opinion with some limited consensus among groups of people.
My feeling is that any absolute morality that might exist is useless to humans if God doesn't make them known to us. Humans sometimes claim to have absolute morals, but it is generally only a justification for persecuting those who disagree with them.
Ahhh okay, very clever Christian argument (absolute morality). So let's see if I can tackle this issue, this type of assertion seems to be a trap.
There is a street preacher I have seen on youtube named Sye Ten Bruggencate that makes this argument I think. I have seen his videos before and he states do absolutes exist, and are you absolutely sure, then ties it all to God being a creator.
So let me tackle this issue now that it is clear what is going on.
Firstly, monotheism (belief in one God) develops historically from polytheism (belief in many Gods), so the monotheist that asserts this claim does so on a premise of Christian philosophy, but it fails. It fails because, since monotheism develops from polytheism.
Secondly, and I firmly believe we were engendered (created if you'd like) creation itself is a reflection of a creator or Gods who engender. Meaning the term "absolute" itself is then irrelevant, because what we see in the earliest creation epics are Gods given power to create mankind, these are Gods of one God (children of one God if you will).
But let's say you stick to your Christian guns and state we were absolutely created by a perfect God. This leads me to think of the verse talking about how we were created in his (God) "image" and "likeness", meaning that since we are living breathing human's, and since there is no difference in the concrete nouns "image" and "likeness" then God must also be corporeal and humanoid, this is a huge problem concerning idol worship, hence by our very being we are violating the 2nd commandment, prohibiting us from idol worship; I posted the entire argument before, do you care to read it?
However, let's say you went the atheist route and stated "relative morality", generally speaking morality is dictated by society so in that case it is morality as a whole that is dictated by society. So if your action is in violation of societal laws then you face consequences.
Let's say you went the Christian monotheist route, well if we were all created then by society establishing what it thinks morality is based on bible folklore then by simply being created in his "image" and "likeness" our morality reflects our creator (see my above posting on "image" and "likeness").