I understand egalitarianism as either (a) no one has a privilege that everyone else doesn't also have, (b) everyone has direct access to what they need, (c) everyone has direct input in decisions that affect them, (c) diversity exists without power hierarchies and exploitation of labor.
Anthropologists distinguish between egalitarian societies, ranked societies, and class-based societies, and I find these distinctions useful. I don't like the term "equality" because to me it can too easily become a vehicle for authoritarian conformity.
Two texts I find useful here are "Egalitarian Societies" by James Woodburn, and "How Hunter-Gatherers Maintained Their Egalitarian Ways" by Peter Gray, both available online.
The wikipedia entry for "egalitarianism" has mentions one definition as "a social philosophy advocating the removal of economic inequalities among people or the decentralization of power", so we can see obvious parallels to anarchism.