In fact a group of (small) islands, near Lesbos in the eastern Aegean (Barrington Atlas map 57 grid E2). (So, correctly, Harpokration s.v. Arginousai, presumably the immediate source of the present, unimpressive entry.)
Site of a celebrated seabattle between the Athenian and Spartan navies in 406 BCE; cf. epsilon 3234 and see generally OCD(4) p.148, under 'Arginusae'.
The -nn- version of the name is confined to lexica and scholia.