I spent a lot of time travelling to The Netherlands, Argentina, France, China, and Mexico on business before becoming disabled.

It literally means anonymous society, because it's actually owned by the stockholders, who, as in the US, are anonymous to the general public.

Just in case you travel:
Société anonyme S.A in French,
Società anonima (SA) in Italian Switzerland,
Sociedad Anónima S.A. in Spanish
Società per Azioni (S.p.A.) in Italian,
Naamloze Vennootschap (N.V.) in Dutch