Definition
Virtue ethics is the ethical framework that asks not "what is the right rule to follow?" (deontology) or "what produces the best outcomes?" (consequentialism) but "what kind of person should I be?" The right action in any situation is the action a person of good character would perform — and good character is neither innate nor accidental. It is developed through habitual practice: each courageous act makes you more courageous; each just decision makes you more just.
Aristotle is the classical architect of virtue ethics, but the Stoics produced one of its most rigorous and practically-oriented forms. Stoic ethics identifies four cardinal virtues — wisdom, courage, temperance, and justice — and argues that they are the only genuine goods. Everything else (health, wealth, reputation, even the wellbeing of those you love) is a "preferred indifferent": good to have, but not constitutive of a good life, and therefore not worth sacrificing virtue to obtain.
Why it matters
The four virtues and their interdependence
Virtue ethics vs. the alternatives
Against deontology
Deontological ethics (most famously Kant's categorical imperative) grounds morality in universal rules: act only on principles you could will to be universal law. Virtue ethics objects that this approach cannot navigate the infinite situational complexity of real moral life. Rules cannot be written precisely enough to cover all cases, and rigid rule-following in unusual circumstances can produce obviously wrong results. A person of good character exercises practical wisdom (phronesis) — situational judgment about how to apply general principles to specific circumstances.
Against consequentialism
Consequentialist ethics (utilitarianism, for instance) judges actions entirely by their outcomes. Virtue ethics objects on two grounds: first, outcomes are often beyond our control, which makes morality hostage to luck; second, a focus on outcomes alone can justify acts that corrupt character — small dishonesties, small betrayals, "justified" cruelties — and a character built from such acts is not a good character regardless of what it produced.
The Stoic synthesis: virtue is the only genuine good because it is the only thing fully within our control. Outcomes matter, but they are not the source of a good life. The archer who aims well and shoots well has done their moral work, even if the wind changes.