Anarchy is a state with no government and no order. Nobody in charge, and nothing to appeal to.
Everyday use means simply chaos, so describing a classroom as anarchy is a complaint about noise. The political sense is more careful, since anarchism is a serious tradition arguing for a society organised without a state, which its supporters insist is not the same as disorder. That gap between the everyday and the political meaning is where most arguments about the word start. The adjective anarchic usually means wildly disordered.
New Latin
anarchia
English, today
anarchy
From New Latin anarchia. From New Latin anarchia, from Ancient Greek ἀναρχία. by surface analysis, an- + -archy.
Etymology from Wiktionary, CC BY-SA