Objective morality is the idea that a certain system of ethics or set of moral judgments is not just true according to a person's subjective opinion, but factually true. Proponents of this theory would argue that a statement like "Murder is wrong" can be as objectively true as "1 + 1 = 2." Most of the time, the alleged source is God, or the Kantian Categorical Imperative; arguably, no objective source of morality has ever been confirmed, nor have any a priori proofs been offered to the effect that morality is anything other than subjective. Kant ultimately fails, because he is perceptibly committed to Christian morality, which guides his arguments. He is nothing like the Nietzschean Over-human.
The moral principles that people claim to be "objective" usually coincide very well with what they feel subjectively to be true. When pressed to provide justification, the person in question will usually just fail to understand that morality might not be objective, and might consequently grow increasingly doubtful or hysterical as the subjective bases of their arguments are progressively revealed, as has been observed in recent times.
Most of the objective morals promoted today in the West are grounded in Christianity. Among Christians, it follows from the ideas of inherent human sinfulness and original sin that one's subjective moral instincts must be categorically classed as evil. Thus, say the Christians, one needs an external, objective source for morality. And — speak of the devil — there is such an external, objective source to be found at a nonspecific location in the sky, sitting on a throne.
The Catholic Church originally admitted several sources for such morality, including human reason; but at the Protestant Reformation, when the principle of "total depravity" was promulgated, human reason became very dodgy and the Bible became the only source that was not suspect. Hence, we see creationists arguing that there are no meaningful morals if Genesis 1 is not true to the letter.