Anarchy is defined negatively, but that negative could only exist if a positive were present: a functioning system of communication and decision-making structure that would enable a body of people to arrive at group decisions without utilizing a hierarchy of people over other people. (Only the latter part is definitively anarchy, but the preceding part is necessary if it is to exist in any persistent manner).
What is to be gained by having one’s organizations function without a hierarchy of decision-making authority?
An end to stupid perpetual power struggles.
An end to people making decisions for you that you have to put up with.
An end to the tendency for useful perspectives and insights not being taken into account as a result of the people who have them not being in the proper positions of decision-making authority.
An end to the initiative-draining rigidity inherent in conventional structures of authority (the old “you can’t fight city hall” thing).
Or, in more lurid terms, an end to tyranny, oppression, institutionalized coercion. The possibility of standing as an equal among equals, having no boss, no superior officer, no one over you with authority to tell you what you must do.
Also a solution to ossification and long-range inefficiency and low civil & cultural participation.