ok, I typed out a definition like three times, but I'll just go with wikipedia
Anarchist communism is a form of
anarchism that advocates the abolition of the
State and
capitalism in favor of a horizontal network of
voluntary associations through which everyone will be free to satisfy his or her needs.
Anarchist
communism is also known as
anarcho-communism,
communist anarchism, or, sometimes,
libertarian communism. However, while all anarchist communists are libertarian communists, some libertarian communists, such as
council communists, are not anarchists. What distinguishes anarchist communism from other variants of libertarian communism is the former's opposition to all forms of political power, hierarchy and domination.