The Moral Zeitgeist is a term used by atheists to describe the evolution of morality. Proponents of a moral Zeitgeist believe that morality evolved to help what they believe to be our ape-like ancestors survive in large groups as social animals. This theory suggests that moral acceptability is chosen by the masses. As people's view of what is morally right and wrong changes, the moral Zeitgeist is said to "shift." This position is rejected by Creationists and most Christians.
Slavery, which was taken for granted in the Bible and throughout most of history, was abolished in civilized countries in the nineteenth century. All civilized nations now accept what was widely denied up to the 1920s, that a woman's vote, in an election or on a jury, is the equal of a man's. In today's enlightened societies (a category that manifestly does not include, for example, Saudi Arabia), women are no longer regarded as property, as they clearly were in biblical times. Any modern legal system would have prosecuted Abraham for child abuse. 
The moral Zeitgeist is believed to be independent of any religious principles. However, it is freely admitted that the moral Zeitgeist changes universally and sometimes very quickly. This suggests to its proponents that something effects its changes, however, nothing has yet been found to do so. Detractors of the theory say this is simply Atheist avoidance of admitting the power of God.
The Evolution of Morality
The moral Zeitgeist was proposed to explain the evolution of morality. While natural selection favors individuals instead of populations, it has been proposed that it must have been more beneficial to the individuals of the species to behave somewhat morally (No society, not even a small clan of apes, can function well if the members go around killing each other). This is also used to explain why people have a tendency to be more moral to the people to whom they are most closely related.
The changing moral Zeitgeist is believed to be the evolution of morality. Detractors believe the constant change is nothing more than relativists blowing in the wind, never firmly grounded by fundamental, never changing, moral/religious principles.
The Word Zeitgeist
Zeitgeist is a German word meaning "spirit of the times."
The moral Zeitgeist is incompatible with moral absolutism and religious morality. Moral absolutism suggests that actions are either morally right, acceptable, or wrong, regardless of the context. Religious morality suggests that actions are either morally right, acceptable, or wrong based on the religion's teaching (see Buddhism) or the revelations of a deity or deities. The moral Zeitgeist suggests that actions are morally right, acceptable, or wrong based on the opinions of the masses.
Moral Realism and the Moral Zeitgeist
Another view of the moral zeitgeist is that all moral controversy is strictly a matter of factual dispute or pointing out logical flaws in other people's argument. For instance, some people held the empirical premise black people should not be considered humans in an attempt to justify slavery. Once that empirical premise was disproven, and blacks were shown to be just as much humans as other people, that justified equality instead. So slavery is not considered immoral on the moral zeitgeist due to an arbitrary change in popular opinion, but by the refutation of the flawed empirical premise of slavery.
The moral zeitgeist is thus compatible with moral realism, the notion that true moral facts exists. Atheist and secular humanist Richard Carrier, a defender of moral realism, writes
"Thus we can explain all moral controversy and progress. For when we try to argue that someone is wrong about a moral proposition we always find ourselves arguing in either of two ways: either we point out how their understanding of the facts is wrong, or we point out how they have deduced the incorrect values from the actual facts. Both can be valid arguments. For instance, we tell the Nazi that his beliefs, like that Jews are not human beings and that they are plotting to take over the world, are factually false, and therefore his morals regarding the Jews are in error"
"There seems to be a steadily shifting standard of what is morally acceptable... Something... has shifted in all of us, and the shift has no connection with religion. If anything, it happens in spite of religion, not because of it." --- Richard Dawkins, The God Delusion