In ordinary speech, selfishness (also called 'egotism', a word never used in philosophy).
As a philosophical doctrine egoism is either psychological egoism (for which see hedonism), or ethical egoism, which contrasts with universalism and altruism. Like them it is a form of consequentialism, and prescribes that everyone should always act so as to maximize his own happiness or welfare.
Egoism must be distinguished from the absurd doctrine, which has no name, that everyone should maximize the speaker's happiness - but this very distinction leads to an objection to egoism: can I consistently prescribe egoism to you, since I shall be encouraging you to act in your interest and not in mine? Also seeking my own happiness may not be the best way of achieving it.
However, sometimes 'enlightened egoism' is advocated as a means rather than an end, on the grounds that for everyone to pursue their own interest will maximize the general prosperity.
H Sidgwick, The Methods of Ethics, book 2 (1874; 7th and final edn 1901)