In the anarchist approach, equality means having the same access to resources and rights, to power, education, decision-making and so on.
Where freedom is how able an individual is to make decisions and voice their opinions, equality is how external factors affect that freedom. It is how much capacity that person has, as affected by social pressures, access to education, resources, etc. It is also about seeing individuals as individuals and not pre-judging them because of some aspect about them they cannot change, about being open minded to let them be as they are.
Generally it is applied to gender, race, sexuality, age, etc. For an anarchist it goes beyond these, to be applied in all situations where there is discriminatory access to resources or power. All individuals should have equal access to their share of available resources and share equal responsibility and participation in all decisions made in their name
Equality is the basis of passive social relationships, that is, how we relate to all members of our society, strangers and friends alike. It underpins the society that we want to live in. If notions of equality are superficial, then the society itself will be hollow, allowing the oppression we sought to be rid to continuing in subtler forms.
It demands that you do not see yourself as more deserving or more important over another simply because of who you are. It tempers the selfishness of pure libertarianism, and ensures that asserting our freedom does not come at the expense of others. The logical conclusion of is a tension between self-interest and society’s interest.
Equality does not require that you have to like everyone, but it does imply that there has to be a basic respect for the needs and freedoms of other people in your community. That means sharing power and resources, ensuring they are distributed equally, not acquiring them in order to protect individual freedoms. The needs of the wider community are just as important. Thus, it imposes a need for awareness of the impact of our actions and ambitions.
For example, when we talk about discrimination it is essentially about different people not having access to jobs or equal pay simply because of something about them over which they have no ability to change. It requires us as anarchists to look people in the eye and deal with them honestly and as individuals with their own needs and desires, such as talking directly to disabled people instead of their carers.
Discrimination implies there exists a justification for an inequality. Anarchism resists this as a fundamental betrayal of principle of equality.
This analysis can be extended beyond individuals to considering relationships between different communities and even different cultures.