The goal of anarchism
Anarchism envisages a post-state society of autonomous individuals and of voluntary, non-coercive social aggregates (such as communes and co-operatives).
There is scope for government in the sense of a co-ordinating body but this itself will be a voluntary, non-coercive social aggregate. A govermment can have a juridical function : to promulgate, administer, and to determine breaches of laws and to settle disputes about the interpretation of laws. But in the exercise of this function, no coercion is present or is permitted.
No force or coercion
An anarchist society cannot accommodate power in the sense of force or coercion.
Force : A has the power of force over B when A gets (or can get) B to do X regardless of B's volition (e.g. A controls or can control B by physical superiority - 'brute force')
Coercion : A has coercive power over B when A gets (or can get) B to do X by threat (e.g. A threatens to make B worse off relative to some baseline if B does not do X : lots of conditions have to be added such as that A must have certain motives, intentions and beliefs, else what appears to be a threat is not actually so, also B must believe that A's threat is credible and must do X because of A's threat and not because s/he was going to do X anyway, plus the 'worse off' must refer to a state of affairs that B considers not trivial but seriously detrimental to his or her interests)
Forms of power
However, I always thought that the total elimination of power is not the purpose of anarchists.
That's dead right.
To remove force and coercion is not to exclude power from society. Without force or coercion I can still exercise power over you by the use of persuasion or manipulation or by charisma or strength of personality. To suppose that such elements could all be removed from an anarchist society appears excessively optimistic. There is also the power of public opinion - the serpent in the anarchist garden as it has been called.
Alan Wertheimer, Coercion (Studies in Moral, Political and Legal Philosophy), ISBN 10: 0691077592 / ISBN 13: 9780691077598
Published by Princeton Univ Press, 1988.
Robert Nozick, 'Coercion', White Morgenbesser (ed.), Philosophy, Science, and Method: Essays in Honor of Ernest Nagel. St Martin's Press. pp. 440--72 (1969).
David E. Apter & James Joll ed., Anarchism Today (Studies in comparative politics), ISBN 10: 0333120418 / ISBN 13: 9780333120415
Published by Macmillan, 1971.
I am unable to reference the 'serpent' quote : apologies.