What is the real meaning of κόλασις αἰώνιος (kolasis aionios)?

This phrase is a false friend.

In Modern Greek, it sounds like “eternal hell”. In Modern Greek it would in fact be αιώνια κόλαση: the word order is slightly more fixed, adjectives before feminine nouns must have an -a and not an -o ending, and the third declension has been merged into the first.

In Ancient Greek, it is not eternal hell. It is eternal punishment, eternal chastisement. That particular word for punishment was used a lot in the New Testament and Christianity for what happens to sinners after death; so it was transferred across to the place where that punishment happens. Lampe’s dictionary mentions that meaning in a couple of passages in the 4th century AD, but they still look like meaning just “punishment” to me. The earliest examples Kriaras’ dictionary of Early Modern Greek has meaning “hell” are from 16th century Crete.

A semantic dictionary of late mediaeval Greek remains a desideratum; Trapp’s Lexikon is wonderful, but as Trapp himself admitted to me, it simply doesn’t do semantics. (In fact, it skips words that existed already, because it’s about new words; there is no entry in Trapp for kolasis.)