1. Anarchism opposes all forms of hierarchy and domination. That is, all situations in which there is an imbalance in power, such that one person's needs and desires are subordinated or treated as less than equally important to someone else's. Justice is not the application of a rigid set of laws, but the resolution of conflicts in a way that treats everyone's interests as equal, arrived at through direct reconciliation between those in conflict by reasoning together.
2. Anarchism opposes authority and government, the state of affairs (a subtype of the first) where people are told what they can and cannot do, how they can and cannot live, and in general controlled and limited and policed. Anarchists view government and authority as fundamentally oppressive, because it necessarily rests on hierarchy and domination, which in turn rests on violence, and also because it prevents the operation of justice as defined in the previous point.
@alexispurslane I'd also add that this includes both explicit *and* implicit forms of power imbalance and 'government' - as it's unfortunately not obvious to a lot of people that capitalism also falls under that umbrella, despite its "freedom of choice" propaganda to the contrary.
@joepie91 Agreed!