What exactly does this phrase mean? I read it in a news article sent by a friend but apart from knowing that it was one of a trilogy of novels its usage seems to have a wider context.
Karagatsis' readers can give you details. This is a title that Karagatsis gave to his first three novels. According to Wikipedia:
His first three novels (Colonel Liapkin, Chimaera and Junkermann) compose a trilogy named Acclimazation under Apollo, about foreigners who live and work in Greece. Karagatsis sets these books in modern, cosmopolitan Greece, in contrast with the stereotype that Greek life is conservative and countrified. https://en.wikipedia.org/wiki/M._Karagatsis