The literal definition of anarchy is: without ruler.
It does not mean:
- Chaos
- No rules
- No organization
If you're asking "But how will society function without government?", you should first acknowledge what a government truly is. It is a ruling class that demands your obedience even if you disagree with some of its laws or how it spends your money. If you dare to disobey "the law", or resist being extorted (taxed), it will violently punish you by throwing you in jail or even killing you if you use force to defend yourself from the punishment. In short, without a government, society would function similar to how it functions now, except there would be a lot less oppression, extortion and war.
These great videos by Larken Rose also break down this topic in a way that is easy to understand: