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.
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 to an unprecedented degree, 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.
 The Murder Argument
A common argument in favor of objective morality is to assert that all societies agree that murder is wrong. However, murder is by definition the unlawful taking of life, so any agreement is merely that people within a society should obey the rules of society. For the argument to have any validity, all societies would have to agree on which types of killing constitute murder, but even a cursory review of human history shows this is not the case. Infanticide, which one might think would be universally reviled, was perfectly acceptable to the Romans and Spartans. Human sacrifice has been practiced by cultures around the world, as have judicial executions. The slaughter of civilians in war was widely accepted until fairly modern times. Some cultures did not consider it murder to kill people from other nations. In the Edo period, samurai had wide latitude to kill peasants over the slightest discourtesy. Unless there is at least one type of killing that is universally considered to be murder, it cannot be argued that all societies agree that murder is wrong in any meaningful sense.