The definition I use is 'a system lacking a state or ruling elite.' If you want to include anarcho capitalism you probably want a more general definition though.
I think I derived this definition from David Graeber's work.
Also some people choose a definition that emphasizes the process rather than the features. Those kinds of definitions are like 'removing unjust hierarchy or domination' or something to that nature.
I would argue that definition is far too broad. I would define anarchism as a society in which the amount of power that any person can have over another person is severely limited. Not only would government have to be greatly weakened, but property rights would have to be greatly weakened, corporations, churches, political parties and all kinds of other organizations would have to be broken up and democratized.
I think I derived this definition from David Graeber's work.
Also some people choose a definition that emphasizes the process rather than the features. Those kinds of definitions are like 'removing unjust hierarchy or domination' or something to that nature.