What we traditionally call morality is a multilayered phenomenon, with innate, cultural and religious components. Understanding that fact is the basis of understanding secular morality.
Every human is born with an innate basic moral sense. This is our “conscience”, our sense of justice and fairness, and our feelings of right and wrong that help us get along in society. Feelings about murder, theft, incest, lying, and many other behaviors are part of the innate moral sense. These feelings are common to, and thus transcend, all individuals, cultures and religions.
All cultures have developed elaborations of the innate moral sense. That is, all cultures have ways to detect, express, and react to situations in which the moral sense is involved. Words and sayings, rewards and punishments, rituals and other behaviors are some of the elaborations of what individuals know instinctively. Obviously, cultures tend to diverge in their elaborations of the moral sense.
All religions go further in their elaborations. In particular, they ascribe the origin of the moral sense to the supernatural. This is the usual consequence of detecting a very real phenomenon, but having no knowledge of its source or cause. Thus, religious elaborations of the moral sense include a supernatural being to appeal to, and to propitiate.
In this and other ways, religious elaborations of morality tend to diverge from the reality of the moral sense, producing behaviors and beliefs that have little or nothing to do with actual morality, but which confuse, complicate, and even contradict it. There is, for example, no genuine moral imperative to be circumcised, nor to avoid eating meat on Fridays, nor to pray in a certain direction several times a day.
Secular morality consciously rejects the religious elaborations that obscure the innate moral sense, and that ascribe supernaturalism to it. Secularism also tends to peel away some of the cultural elaborations, while recognizing that we have to get along in the culture in which we find ourselves.
In particular, secularism acknowledges that the moral sense is innate (not god-given), that it is human-centered (not god-centered), and it acknowledges the variety of the human condition (not an abstract ideal). In other words, the goal of morality is to guide individual human behavior toward human social harmony.
Secular morality is simpler and more realistic than religious morality. Because it operates in the human realm, not the supernatural, it operates in the realm of the knowable and possible, the here and now. It has another very important advantage: it is far more universal in its applicability.
Religious elaborations of morality are essentially arbitrary definitions of in-group versus out-group beliefs and behaviors. Unfortunately, the violation of an in-group behavior might be considered a sin, even a mortal sin. This means that members of an out-group are automatically sinners in the eyes of the in-group, and thus not subject to the protections of the in-group. Hence religious hatreds and warfare tend to be a part of religious morality by definition. Not so with secular morality.