George Lakoff defines relativism in his book "Metaphors We Live By", as the rejection of both subjectivism and objectivism in order to focus on the relationship between them, i.e. the metaphor by which we relate our current experience to our previous experience.
The concept of relativism has importance both for philosophers and for anthropologists, although in different ways. Philosophers explore how beliefs might or might not in fact depend for their truth upon such items as language, conceptual scheme, culture, and so forth; with ethical relativism furnishing just one example. Anthropologists, on the other hand, occupy themselves with describing actual human behavior. For them, relativism refers to a methodological stance whereby the researcher suspends (or brackets) his or her own cultural biases while attempting to understand beliefs and behaviors in their local contexts. This has become known as methodological relativism.
Elements of relativism emerged at least as early as the Sophists.
One argument for relativism is that our own cognitive bias prevents us from being fair as a "subject" observing anything with our own senses, and a notation bias will apply to what we are told exists anywhere outside these senses. Accordingly, we are left with a culture bias shared with other trusted observers, and can never expect to completely escape that in our lifetimes. Skeptics argue that subjective certainty and concrete objects and causes are part of our everyday life, and that there is no great value in discarding such useful ideas as isomorphism, objectivity and a final truth.
Followers of Ayn Rand claim the term "Objectivism" to describe her philosophy of maximizing individual capital at expense of all others - on the grounds that all good comes from trusting the productive, creative and free person. Although they would likely differ with Lakoff's characterization of "objectivism" as a "straw man", it is clear that Lakoff intended at least some criticism of capitalism in his early work, and some support of moral relativism (which Rand despised). To a lesser degree his criticisms apply also to Karl Popper, Kant or Aristotle.
Another important advocate of relativism, Bernard Crick, a British political scientist, wrote the book In Defence of Politics (first published in 1962), suggesting the inevitability of moral conflict between people. Crick stated that only ethics could resolve such conflict, and when that occurred in public it resulted in politics. Accordingly, Crick saw the process of dispute resolution, harms reduction, mediation or peacemaking as central to all of moral philosophy. He became an important influence on the feminists and later on the Greens.
An extremely common argument against relativism uses an inherently contradictory (self-stultifying) notion: The statement "all is relative" is either a relative statement or an absolute one. If it is relative, then there must be some absolutes in the world. If the statement is absolute, on the other hand, then it provides an example of an absolute statement, proving that not all truths are relative.
The latter argument forms one of the first in reply to relativism, and needs more explanation.
You can reply to that by saying that only one thing in the world is absolute: relativism. Thereby solving this dilemma. This is a softer take on relativism. It says that the argument presented above is correct in a way. Not all statements are relative, but the only statement that is not relative is a statement "The only thing that is absolute is that all things are relative." This preserves relativism for all intents and purposes as it is applied to the real world, although in a weaker sense.