| | I agree, Luke. Leonard Peikoff's thumbnail definition is concise, precise, and wry. I checked Philosophy: Who Needs It? and For the New Intellectual and neither held much more insight. The easy answer is, indeed, that utlitarianism mandates that we act to achieve the greatest good for the greatest number.
But like much else, it is a bit more complicated. In addition to Wikipedia (of course), the Stanford Encyclopedia of Philosophy (here) has a detailed explanation. Not surprisingly, the philosophy has its adherents, to be found at www.Utilitarianism.org, of course. Read as much as you please.
Allow me to add one note. We look at these as social ethics. In fact, Bentham's "hedonistic calculus" was also intended for personal use. In order to decide on a course of action such as the purchase of a car, you create an accounting T-ledger and balance the Assets against the Liabilities. It is, indeed, one way to approach decisions, perhaps even inducing a dispassionate appraisal.
Intense, long, certain, speedy, fruitful, pure—
Such marks in pleasures and in pains endure.
Such pleasures seek if private be thy end:
If it be public, wide let them extend
Such pains avoid, whichever be thy view:
If pains must come, let them extend to few.
Bentham's Mnemonic cited in "Felicific Calculus" Wikipedia here
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