I can't say I've testing too much, but my understanding of ages is as follows:
Age of Myth: Occurs early, when there are a lot of megabeasts and the like running around. Age when the creatures of myth rule the world.
Age of Legends: When a lot of the megabeasts have been whipped out, but there's still a lot of them around.
Age of Heroes: Occurs when there are a lot of elite/legendary military around. As I recall, somebody was able to show that you could actually TRIGGER the Age of Heroes in Fortress mode by building a large enough military(or whipping out a couple extra megabeasts).
Age of foo: Occurs when foo becomes dominant in the world by a wide enough margin. Apparently works for anything...civs if they become powerful enough relative to everyone else and creatures if a single one rampages long enough.
Age of Three Powers: Never seen it personally. Supposedly occurs when there are three dominants.
Age of Civilization: Read about it somewhere on the forums...apparently occurs when humans are the only thing left, no fantasy creatures at all.
Golden Age: Seems to be the point when the megabeasts are largely/completely gone and all of the civilizations are flourishing.
Age of Twilight: Occurs when civilization recedes. The world is literally coming to an end at this point...or at least all civilization is, anyway.
Also, any of these can theoretically repeat, ie Second Golden Age, Fourth Age of Myth, Fifth Age of Heroes. Getting some of them to repeat is tricky, though. This can be taken to some MAJOR extremes...like the
24th Twilight Age in the one example I saw from a really old thread. Getting the Age of Twilight to repeat that many times must have been fun.