This is the root for the English word eon, yes? Or rather, the older Greek word that led to this modern Greek word?
I saw the connection with eon as well. In greek does it always mean century or can it also mean something like the English word, a very, very long but undefined period of time?
It means century most of the time. It can also mean a defined period of time "age of technology"="εποχή/αιώνας της τεχνολογίας", and in geological periods "Mesozoic=μεσοζωικός αιώνας". It can have the meaning of the English word eon, if used in plural, but that would mean "centuries" (which is a long and undefined period of time)
I feel "the age" should be included as well; though it's a bit antiquated, it is still used to mean century. After all, "καὶ εἰς τοὺς αἰῶνας τῶν αἰώνων", is usually translated to "and unto ages of ages"