It's very well explained by evolution. Some animals species evolved to be social, namely to live and cooperate together. This gives a lot of survival advantages, from having sentries and protectors against danger, to sharing food, to specialized roles, to having communal help raising your young.
In social species like wolves, monkeys, certain bird species, dolphins, gophers, horses, etc, there is natural selective pressure to evolve behaviors that benefit the group, and selective pressure against behavior that harms the group. Individuals that act against the group will usually be ostracized from the group, upon which they are alone and typically die before reproducing. Individuals that are viewed favorably by others will be more likely to reproduce more. Human teenagers, for example, who are biologically at a prime reproductive age, are especially sensitive about being accepted by their peers.
For these reasons, we have evolved traits like empathy, guilt, a sense for the motives of others, and a sense of fairness. As we would expect, these traits are expressed on a spectrum among individuals, from psychopaths on one end to empathetic, gentle helpers on the other. Just like people can be very short or tall on the spectrum of physical height.
The larger the brain of the social species, the more complex the moral behavior we can observe. Naturalism explains it all very well. There are for example scientific studies comparing the capacity to sense fairness in different animal species, and we see it becoming a more complex dynamic going from dogs, to apes, to humans.
It's true that some of us feel like there is an "objective morality" but I've never been able to pin down a theist on what one of these objective morals actually is. Really, I challenge you to find any moral position that everyone agrees on, and that no one has ever violated. There are definitely moral stances that virtually everyone agrees on, but this just means these notions are central to virtually all forms of successful socialization.
