Errico Malatesta, Anarchy - "The word Anarchy comes from the Greek and its literal meaning is without government: the condition of a people who live without a constituted authority, without government"

Peter Kropotkin, Anarchism - "Anarchism is the name given to a principle or theory of life and conduct under which society is conceived without government - harmony in such a society being obtained, not by submission to law, or by obedience to any authority, but by free agreements concluded between the various groups [...]"

The main point is a lack of vertical hierarchy, that nobody is being subjugated or forced. For a society to function, it needs cooperation, and anarchical coorperation means that it's done willingly by all the parties involved, without any compulsion. You can still have structures (as in roles people play in a society). Orwelll wrote in "Homage to Catalonia" how the army he was in had regular soldiers and officers, but the officers couldn't "order" the soldiers to do anything, and they often argued and explained why they needed the soldiers to do whatever. A wild free-for-all where some strong and brutish people can form a gang and do whatever they want with others is how some anarchists see governments.

So it's technically true that there are no "laws" because there is no government to punish you if you don't follow them, and there's no vertical structure where someone is your boss who you must obey, but people might get a wrong picture with just that, so I provided a bit more context. I'm not an expert on anarchist theory by any means, but it's not Hobbes' natural condition of mankind.

Anarchism and anarchy are not the same thing.