To the Moon! Apparently that's a tradition in the Final Fantasy series.
The trailer is a bit opaque, as the main thrust of the story is more that it finishes the major Zodiark/Hydaelyn story that has been ongoing since launch. Apparently a new story will start with Patch 6.1. As well, I think what's actually going on is a bit murky in-game.
The new class is Sage, which looks like some sort of sci-fi Healer. I understand it will be a shield healer along with Scholar. Meanwhile Astrologian will be reworked to be closer to White Mage as a regular healer, giving two of each type.
There's another new class as well, but it will be revealed in May. I believe the expansion proper is launching in September.
Truthfully, though, I haven't played FFXIV since 5.3, so I'm probably not up-to-date on what is happening. On the one hand, it probably would be good to finish the complete story. On the other hand, I don't really like the current main villain, Zenos. I wish he had stayed dead in Stormblood.