Moral realism is simply the idea that obligations exist objectively.
There are real, subject-independent duties that we must accept in order to act morally. These duties are features of reality. They exist independent of perceiving minds, social constructs, cultural norms, etc.
They exist independent of our knowledge about them or our judgments of them. They are there to be discovered.
If all humanity died off, there would still exist a duty not to murder. Just as if all humanity died off, a square would still have four right angles.
Moral realism says moral duties exist necessarily, i.e., they cannot fail to exist. Duties and obligations exist in moral reality as such, in a straightforward sense, and cannot be reduced to ideology, social phenomena, illusions, psychological states, masks, rhetorical devices, preferences, opinions, judgements, expressions of taste, language games, expressions of emotional states, evolutionary adaptations, etc.
If moral reality exists, then all attempts to explain it away using such terminology are just that, attempts to explain it away.
(Note: This is a working definition, and I reserve the right to revise it.)