Moral relativism is the view that there are no objective ethical truths, that moral facts only hold relative to a given individual or society. According to this ethical theory, what is morally good for one person or culture might be morally bad for another, and vice versa: there are no moral absolutes.
The individualistic form of moral relativism, according to which morality varies between individuals, is called ethical subjectivism. The societal version, according to which morality varies between cultures, is called cultural relativism.
Objective truths are truths that hold independent of our beliefs or perceptions. The Earth orbits the Sun, for instance, whether or not we believe that it does. It was true that the Earth orbits the Sun even when the prevailing view was that the Sun orbits the Earth.
A subjective truth, on the other hand, holds at least in part because of our beliefs or perceptions. Whether peanut butter tastes good, for example, varies from person to person; for some people this is true, for others it is false. Whether peanut butter tastes good, then, is a subjective matter.
Moral relativism holds that ethical truths are of this latter kind. According to moral relativism, ethical truths are subjective rather than objective. This means that whether lying is wrong, for example, can vary from person to person or from culture to culture. It may be that for some people, or in some cultures, it is wrong, but that for other people, or in other cultures it isn‘t.
In one mild form, moral relativism can seem obvious. Of course different people have different moral obligations: I have a duty to pay my credit card bill; you do not. Each of us is in different circumstances, and those circumstances affect what we ought and ought not to do. Morality is therefore relative to circumstances.
What is usually meant by moral relativism, however, is not merely that moral truths are relative to circumstances but that moral truths are relative to people or groups of people. Moral relativism holds that two different people (or groups of people) in identical circumstances can, for no other reason than that they are different people (or groups of people), have different obligations. This is a much stronger claim than that morality is relative to circumstances.
The credit card example, then, is consistent with moral absolutism. The absolutist can explain the fact that although I have a duty to pay my credit card bill and you do not, there is nevertheless an objective moral rule that applies to both of us: repay your debts. If it were your bill, then you would have to pay it and I would not. Anyone in my situation, the absolutist will hold, would have a duty to pay the bill, irrespective of who they are.