Ethical subjectivism is, as it sounds, the view that moral judgments have no objective basis but are based on subjective factors such as emotion/sentiment and desire. The observation that moral judgments are ordinarily rooted in such subjective factors is an empirical one, albeit one that would be difficult or impossible to falsify, even on an individual-by-individual basis. My own anecdotal experience suggests that this observation is often true, though I have encountered many people who would vociferously deny that their moral views are based on subjective factors.
As a general rule, however, I think it is safe to say that most of the moral views that most people in most societies hold are ultimately based on sentiment and/or the desires of those who first advocated the moral views in question. Now of course, very often people do not believe that the dominant moral views of their society or their personal moral views are based on subjective factors such as sentiment and desire, so any claim that they are nonetheless based on subjective factors will likely be rejected by most people in the absence of persuasive arguments (or indeed, even if persuasive arguments are made for ethical subjectivism).
The most famous ethical subjectivist was probably David Hume. He argued forcefully that people’s moral views are always based on sentiment or emotion and has thus been labeled an emotivist. In brief, his argument is that it is always possible to defend any moral viewpoint using reason, but with respect to morality reason alone leads to an impasse. Furthermore, reason alone is not enough to cause a person to act or prevent a person from acting; only the emotions can excite a person to act or not act; because moral principles can excite a person to act or not act, they must be based on emotion. It is not that Hume thought there was no place for reason in moral discourse; he just believed reason is and ought to remain subservient to emotion/sentiment in moral reasoning and moral discourse. Hume was the first philosopher to make the distinction between facts and values (with the latter not being possible to derive from the former) and formulated the previously discussed is-ought problem based on this distinction.
Generally speaking, Hume’s reasoning is persuasive. The is-ought problem has never been resolved by any moral or ethical philosopher since Hume’s time, though many have tried to defend moral realism and show that moral principles can be derived from observable natural (or even supernatural) properties, or that moral principles are sui generis and can be known or observed independent of any other natural (or supernatural) phenomena.
But ethical subjectivism is problematic in some ways. First, as a meta-ethical theory, its proponents often claim that it explains the meaning of moral terms. Perhaps it explains the ultimate meaning of moral terms, but for the most part people do not intend to convey subjective judgments or preferences when they use moral terms like “good” and “bad,” but properties of the world that can be known by all. Again, perhaps people who use terms in this latter way are mistaken, but such people certainly don’t intend these terms to mean what ethical subjectivists believe they mean.
Second, ethical subjectivists very often persist in acting as though moral principles derived from sentiment or another subjective basis are nonetheless binding and ought to be treated as authoritative over how people behave or ought to behave. Hume himself persisted in doing this, though it is possible to wonder whether he did so because he feared persecution by the Church of Scotland. Nonetheless, if moral principles are indeed rooted in subjective factors, then they are in fact not binding on people, at least not by the operation of any natural (or supernatural) law. Now, even if they are rooted in subjective factors, and even if they are believed to be rooted in subjective factors, moral principles can still be imposed by force and can be made “binding” in this sense. But in no sense can they ever be binding in the same way that moral principles rooted in natural law or in the basic fabric of existence, so to speak, would be.
But these criticisms aside, ethical subjectivism provides a convincing explanation of where moral principles ultimately come from. Even if it is difficult or impossible to confirm or falsify the truth of ethical subjectivism empirically, it still provides an explanation that at least fits with my experience and, I believe, with the experiences of many others.