The objectivity of morality can be attributed either to natural or divine sources. For example, Hedonism defines the good as maximal pleasure for oneself while Utilitarianism defines the good as happiness for the greatest number. Both pleasure and happiness are natural features of the world. A Divine Command theory defines the good as that which God commands (via special revelation) so it too would be a fact (a true state of affairs), but a non-natural one. So, regardless of the source of the good, objectivists believe that there are moral facts in the world.
Objectivist generally fall into one of two categories when thinking about the objectivity of moral principles. A radical objectivist (e.g., Immanuel Kant) not only believes that moral principles are objective features of the world, but also that they are inviolable (i.e., there are no circumstances in which they should be overridden by other moral considerations). This strong view of the objectivity of moral values is often known as Moral Absolutism. Views that hold objective moral principles may counter each other or outweigh each other are generally referred to under the more generic term Moral Objectivism.