Here it is, if you want to watch:
Karazhan is the first raid I ever ran - though I only did so twice and got stuck at the Curator both times. Still, I have a lot of nostalgia for that place and was incredibly excited to find out that they were bringing it back (without getting rid of the original version) in Legion.
Blizzard is clearly experimenting a lot with dungeons this time around - Arcway and Court of Stars are both pretty unconventional, and the whole Mythic+ system is an attempt to find a new way to keep dungeons relevant throughout the expansion (my only problem with the system is that it's based on time limits.)
Return to Karazhan is a clear example of this experimentation. Or, one could argue that it's a throwback to something we really haven't seen since vanilla, namely a super-long dungeon (ok, you could argue that Halls of Origination in Cataclysm was the most recent example, but that felt a bit different because bosses 4-7 were all doable in quick succession.)
Return to Karazhan bears similarities with the original raid, but this is clearly not a simple rehash. For one thing, one enters from around the middle of the tower, and the first boss is the Opera Event, with three all-new plays to fight through. Players will clear the lower part of the tower, ending I believe with Moroes, before heading up to face the Curator. After the Curator, things become very different. You'll walk along the ceilings of the library and fight all new bosses. One stand-out example is the Mana Devourer, which is actually a little trash mob, but you've been shrunken down to a tiny size, making it a boss-like challenge. Beating it will restore you to your correct size and allow you to easily AoE down a big pack of Mana Devourers in a kind of cathartic revenge.
The dungeon appears to be filled with secrets, including heavy implications that Nightbane returns as a secret boss. It also appears as if a run will take a couple hours - unlike most modern dungeons which tend to be about a half hour unless you screw up a lot (actually, I'm not sure about that. I'd bet Vault of the Wardens takes a bit more time.)
The length does, I think, imply that pugging this dungeon is probably not a great idea unless you have the patience of a saint. On the other hand, for smaller guilds (or guilds with only a few members who sign up for things...) could look at Karazhan as a place to progress through - treating it like a raid.
I don't think we know what the rewards are going to be for the dungeon. Blizzard has implied that because it is a bigger challenge (and certainly time investment) than other dungeons, that they are willing to make the rewards more attractive. I wouldn't be shocked to see the gear out of here on par with Normal Emerald Nightmare (which to be fair is only ten item levels above 7.0 mythic dungeons.)
I do hope that the gear uses different models than the generic dungeon gear currently available - new stuff would be appreciated of course, but they could easily just use the models from the original Karazhan.
No word yet on when 7.1 comes out, but I'd bet some time before the end of the year.