The simple answer is that Anarchism is an-archos. Archos means ruler, An is a negative. An-Archos = no rulers.
Anarchist believe that in every human endeavor, we will be more pleased with the process and the end results if we organize ourselves in an egalitarian manner on a basis of equality.
A longer answer involves an examination of way in which people are ruled by others including class divisions in society where the rich rule over the poor, or patriarchal relations where men rule over women, or imperialism where one country rules over another, or property relations where one person claims to own something, and rules over who may use this 'property,' when, and for what cost.
Another answer would be a description of anarchist principles like: Solidarity, Mutual Aid, Autonomy, Accountability, Self-Determination, Consent, De-Centralization, Liberation, Equality, Direct Action, and others.