Egoism

Egoism is the ethical position that each person's own life is his standard of value and his own happiness the moral purpose of his life. Objectivism holds a specific version of it, usually called rational egoism, on which what actually serves a person's interest is a question of fact rather than of preference.

“Life can be kept in existence only by a constant process of self-sustaining action. The goal of that action, the ultimate value which, to be kept, must be gained through its every moment, is the organism's life. An organism's life is its standard of value: that which furthers its life is the good, that which threatens it is the evil.”
~ Ayn Rand, "The Objectivist Ethics", The Virtue of Selfishness

Why "selfishness"

Rand chose the word deliberately, and explained the choice in the introduction to The Virtue of Selfishness. The dictionary meaning is "concern with one's own interests". The additional connotation of brutality toward others is not part of the definition but a package deal carried by the ethics of altruism, which treats any concern for oneself as suspect and so leaves no clean word for the person who neither sacrifices himself to others nor others to himself.

The false alternative that results is the sacrificial animal or the exploiter. Objectivism rejects both halves. See Trader Principle for the relation it puts in their place.

It is not a licence

The most common error is to read egoism as "do whatever you want". Rand's position is the opposite, and the structure of the argument is what rules it out:

The standard is man's life qua man: not bare survival at any cost, but living by the means proper to a rational being over a whole lifetime.
What serves that standard is a factual question, answered by reason, not by whim. Acting on unexamined desire is whim-worship, which Rand treated as a failure of egoism rather than an instance of it.
Because man survives by thinking, the person who lives by force or fraud is not practising self-interest successfully. He is living on the results of other people's thinking while undercutting the conditions that make thought effective, including for himself.

This is why the virtues are not constraints imposed on egoism from outside. Rationality, honesty, independence, integrity, justice, productiveness and pride are the means by which a person's actual interests are achieved.

Egoism and other people

Objectivism holds that the interests of rational people do not fundamentally conflict, an argument Rand made in "The 'Conflict' of Men's Interests". Other people are among the greatest values available to a person: as traders, as friends, as objects of love. What is excluded is the demand that anyone's interest be served by sacrificing someone else's.

Benevolence, generosity and even risking one's life for someone one loves are all consistent with egoism, because a value one would not want to live without is one's own value. What would not be consistent is treating a stranger's need as a claim on one's life. See Sacrifice and Altruism.

Common misunderstandings

That "everyone is selfish anyway, since all action is motivated." This confuses the motive of an action with its beneficiary. A person who acts from guilt or conformity is acting on a motive, but not in his interest. Nathaniel Branden's essay "Isn't Everyone Selfish?" in The Virtue of Selfishness addresses this directly.
That egoism forbids helping anyone. It denies that need creates an obligation. Helping people one values, in a context one can afford, is ordinary and expected.
That it means short-range advantage. The standard is a whole life, so an action that gains something today at the cost of one's character, relationships or capacity to think is not in one's interest.
That it is the same as hedonism. Hedonism makes pleasure the standard. Objectivism makes life the standard and treats pleasure as a consequence of achieving values, not as the measure of them.

Discussion

References

Rand, Ayn. "The Objectivist Ethics" and introduction, The Virtue of Selfishness. New American Library, 1964.
Branden, Nathaniel. "Isn't Everyone Selfish?", The Virtue of Selfishness.
Peikoff, Leonard. Objectivism: The Philosophy of Ayn Rand, chapter 8.

External links

Selfishness at the Ayn Rand Lexicon