Hierarchical constructions of power create positions of relative privilege and relative oppression. Anarchism conceptualizes power differently. Instead of power over, anarchism proposes power with, cooperation. This means that social systems and institutions should be based on cooperation. Power would rest in individuals and the collectives they freely associate into.
Equality can have many different meanings.
In regards to our anarchist political philosophy, we speak of equality in reference to power. This doesn't mean we want a new society based on a totalitarian vision of everyone looking and acting the same, in fact we see strength in diversity. Instead we mean that everyone should have equal access to power, to determine how he or she wants to live his or her lives. The best way for equal power to be institutionalized is through different forms of democracy. Democracy is a vague notion, but in general it seeks to empower everyone to have an equal say in decisions that affect their lives.