Playing on the PTR, I got to experience most of an invasion of Azsuna.
The pre-Legion launch event, which saw invasions of Azshara, Northern Barrens, Tanaris, Hillsbrad, Dun Morogh, and Westfall, was a very popular event that got players of all stripes together fighting demons.
In 7.2, similar invasions will occur in the zones of the Broken Isles, though these will work a little differently.
The launch events had four clear phases - fighting a mini-invasion usually in a major town, then a boss in that town, then demons across the whole zone, ending with a tougher boss in town.
It looks like 7.2's will function a bit more like world quests.
When an invasion hits your zone, the current world quests will be put on hold, but new ones will pop up that deal with the invading demons. It appears that these count toward emissary quests, so there's no real downside to an invasion hitting in the middle of your world questing.
Once you clear four of these invasion quests, you'll get a quest to meet with a representative of the zone (in my case, Prince Farondis.) In Azsuna, I was sent to the Temple of a Thousand Lights (near Shackle's Den) to fight my way through the demonic hordes until I defeated some of the demons leading the invasion. I then got a bombing-run quest to destroy a fel conduit. Finally, I was given a quest to do a scenario dealing with the general who led the assault, but it was here that PTR issues were PTR issues, and things got cut short.
The invasion world quests seem to have comparable rewards with normal world quests, though they might be higher quality (I got a pair of 855 - well, 860 warforged - shoulders) but it might simply be that world quest rewards are getting buffed in 7.2 (which would make sense.)
I'm actually a little disappointed that it's not the total free-for-all that it was in the launch event, but given that A: people won't be able to unlock flying for a bit and B: there will be other stuff to do, I guess they can't really model things on the idea that hundreds of players will be swarming the zones to fight the bad guys (though if they wanted to do something similar to the Legion invasions for next expansion's launch, I would not complain.)
I don't know if there's any kind of scaling with gear going on, but the demons invading are rather tough. My Death Knight had Flaskataur-provided Normal tier 19 gear and two legendaries and while I wouldn't say he was ever really in danger of going down, he was definitely not carving up these demons as quickly as he might do with regular Azsuna mobs.