Eye of Azshara - Azshara is here (obviously) and so are all of her naga.
Halls of Valor - Challenge the God King to prove you're more worthy of a Pillar of Creation.
The Arcway - The tunnels underneath the city of Suramar.
Maw of Souls - The hell to the Halls of Valor's heaven, you fight a giant woman on a boat.
Darkheart Thicket - You're off to rescue Malfurion from the Emerald Nightmare.
Court of Stars - A party in Suramar. You're probably going to ruin it.
Vault of the Wardens - Where the Wardens kept the Demon Hunters, and now have turned traitor.
Assault on Violet Hold - A remake of Wrath of the Lich King's Dalaran-based prison, with new beasts.
Black Rook Hold - An impenatrable fortress which, guess what, you're going to penetrate.
Neltharion's Lair - Deathwing's old digs. He doesn't live here any more, but other monsters do.
There's also now four distinct types for each of these dungeons:
Normal - the levelling-up version of the dungeon. Will scale to players in the same way outside zones do.
Heroic - the initial max-level version of the dungeon. Good for some early gear.
Mythic - a harder version of the max-level version. Can't be queued for with a group finder, forcing you to manually find players to party up with.
Mythic+ - not available on launch, Mythic+ is an infinitely scaling version of the dungeon that rewards raid-tier loot. The better you are, the harder the dungeon will be, based on the level of a keystone rewarded at the end. This is meant as a 5-man progression path to equal raids.
WoW: Legion raids
Of course, there's also new raids. These won't be available at launch, coming a few weeks afterwards. The first is the Emerald Nightmare, where you're going in to fix the Emerald Dream and stop the corruption. It takes the Highmaul slot of the expansion's first major raid.
The Nighthold will be next up, and finally see the death of Gul'dan. This is planned for release soon after the Emerald Nightmare, and will reward loot the next tier up. As always, Raid Finder, Normal, Heroic and Mythic difficulties will be available, with the hardest and easiest unlocking after the other two.