a state of mind. anti-authoritarianism, no gods no masters! it's in the heart and soul bro, it's fighting the system, it's an idea, it's a practice, it's change. i would post a huge book on what anarcho punk is, but i just woke up :L
It's a visionary state of mind in which the intellect and the emotional self unite with the impassioned concept of what humanity could be; free of oppression, of prejudice, and of authoritarian systems of thought. If you wish to better understand the anarcho punk mindset a good place to start would be the music. Listen to some Dead Kennedys, Crass, or Minor Threat.