The framework is simple but powerful. For any domain of feeling or action, there is a characteristic way of falling short and a characteristic way of going too far. Courage involves facing danger: the person who faces none is a coward; the person who fears nothing is reckless; the courageous person faces the right dangers, in the right way, for the right reasons. The same structure applies to anger, generosity, truthfulness about oneself, and the pleasures of eating and drinking.
The mean Aristotle has in mind is not a mathematical midpoint between two extremes. Ten pounds of food is too much for a beginner but too little for an athlete; the right amount is relative to the person and the circumstances. What is the mean for me may be excess for someone else. This is why the standard for the mean is not a formula but a person — the person of practical wisdom, who perceives what is appropriate in each situation.
Hitting the mean is genuinely difficult — which is part of why virtue is an achievement. It is easy to be angry or not angry; it is hard to be angry with the right person, to the right degree, at the right time, for the right purpose, and in the right manner. Excellence requires this kind of precision, and precision requires a cultivated perception of what each situation demands.
Aristotle is careful to note that the doctrine of the mean does not imply that there is always a virtuous version of any action. Some actions and feelings are bad in themselves — malice, shamelessness, murder, adultery. There is no right amount of murder, no right person to commit adultery with. The mean applies within the space of actions and feelings that can be performed well or badly; it does not imply that every action has a permissible middle ground.
The doctrine of the mean is introduced in Book II, Chapter 6, and applied to specific virtues throughout Books III and IV of the Nicomachean Ethics.