I'm surprised I haven't seen a thread about this. Or I might have just missed it. This was honestly the first question that came to my mind when entering the new heavensward zones like Churning Mists and Sea of Clouds. I have kept my eyes open for any possible hints to it ingame but I either missed it or there hasn't been any information about it.

And before going with "It's magic/fantasy world." I'd like to point out that the floating islands seem to hint that they either were one large entity.

Churning Mists

Structures and Islands are showing roads that lead to another higher/lower/distant island. Add to that, that floating parts of the building structures are sometimes seen spread around. And then there's the occasional vision of the past that show things very much intact. (examples: The cutscene with the knights of Ishgard after Nidhogg's defeat. Or Nidhogg + Hraesvelgr their conversation.)

Sea of Clouds

Less of the above, but there's a moogle head-shaped island to the north. Which the sightseeing log, hints that moogle might have been the cause for raising this thing in the sky.

Things that both have in common

Crystal like structures below the islands and in the case of Churning Mists, it visibly sticks out in some places above ground.

The Aery

I don't know if anyone noticed the pieces of Allagan debris near the last part of the instance. It really makes one wonder about the entire conflict between Dragons and Allagans. Perhaps they are also linked to the cause of all the floating islands and Azys Lla.

This is mostly me asking the lore community if there are other pieces of information or hints that I might have missed.