Utilitarianism is both a metaethical doctrine, and a theory in normative ethics. Utilitarianism holds, in its simplest form, that "the good" is whatever yields the greatest "utility". Utility has been understood in different ways - happiness, pleasure, preference-satisfaction, etc. - but it is always a naturalistic conception of an individual's good. As a metaethical doctrine, it holds that "whatever yields the greatest utility" is the meaning of the word "good" (thus it is a naturalistic theory of metaethics); while as a normative theory, it merely holds that "whatever yields the greatest utility" is in fact good, whatever the meaning of the word "good" may be.
Utilitarianism was originally proposed in 18th century England by Jeremy Bentham and others, although it can be traced back to ancient Greek philosophers such as Epicurus. As originally formulated, utilitarianism holds that the good is whatever brings the greatest happiness to the greatest number of people.
Both Bentham's formulation and the philosophy of Epicurus can be considered different types of hedonism since they judge the rightness of actions from the happiness that they lead to, and happiness is identified with pleasure. Note, however, that Bentham's formulation is a selfless hedonism. Where Epicurus recommended doing whatever made you happiest, Bentham would have you do what makes everyone happiest.
Utilitarianism is the classic consequentalist theory of ethics, and as such is opposed to non-consequentalist theories, such as deontology or virtue ethics.
Utilitarianism suffers from a number of problems, one of which is the difficulty of comparing utility among different people. Many of the early utilitarians believed that happiness could somehow be measured quantitively and compared between people through a felicific calculus, although no one has ever managed to construct one in practice. It has been argued that the happiness of different people is incommensurable, and thus a felicific calculus is impossible.
Utilitarianism has been criticized for leading to a number of conclusions contrary to 'common sense' morality. For example, if forced to choose between saving one's child or saving two strangers, most people will choose to save their own child. If you ignore your own future happiness or unhappiness as a parent, utilitarianism would support saving the strangers instead, since two people have more total potential for future happiness than one.
John Stuart Mill wrote a famous (and short) book called Utilitarianism. Although Mill was a utilitarian, he argued that not all forms of happiness are of equal value, using his famous saying "It is better to be Socrates unsatisfied, than a pig satisfied."
Daniel Dennett uses the example of Three Mile Island to explore the limits of utilitarianism for guiding decisions. Was the near-meltdown that occurred at this nuclear power plant a good or a bad thing (according to utilitarianism)? He points out that its long-term effects on nuclear policy would be considered beneficial by many (and at least it wasn't a Chernobyl!). His conclusion is that it is still too early (20 years after the event) for utilitarianism to weigh all the evidence and reach a conclusion.
To try to get around some of these cases, different varieties of utilitarianism have been proposed. The traditional form of utilitarianism is act utilitarianism, which states that the best act is whichever act would yield the most utility. A common alternative form is rule utilitarianism, which states that the best act is the one that would be enjoined by whichever rule would yield the most utility.
So, suppose that some situation allows Jill to either lie or be honest. Suppose further that lying would yield the most utility of the three possible acts. Suppose further still that Jill's adhering to the policy of honesty would yield more utility than her adhering to any other available policy. Then act utilitarianism would recommend lying and rule utilitarianism would recommend being honest.
Utilitarianism influenced economics, in particular utility theory, where the concept of utility is also used, although with quite different effect. See also Utilitarian ethics and Utilitarian Bioethics for further consequences of its influence.
John Rawls rejects utlitiarianism as a liberal principle, on the basis that it lacks absolute values. For example, if slavery or torture is beneficial for the population as a whole, it may be justified by utilitarianism. He instead argues that political ethics must be drawn from the original position.