The Vortex Pinnacle resides in the Skywall, the elemental plane of air. Fortunately for you, the only trick to getting there is being able to fly above the zone of Uldum. The instance itself is in the skies in the Southeastern portion of the zone.
In Uldum you will come across the city of Orsis while helping the Ramkahen. Orsis was attacked by wind elementals, servants of Al'akir, who has aligned himself and his armies with Deathwing. Orsis is now left in ruins, but you are able to help out some of the buried citizens in the sand and report back to the Ramkahen on what happened. You also learn that the air elementals took at least one prisoner, and it's up to you to go to the Vortex Pinnacle and save him.
Essentially, the Vortex Pinnacle is just a staging ground for the armies of Al'akir to attack the citizens of Uldum. Thankfully you and your flying mount can take the fight to the army's doorstep and take out some high ranking officials before you eventually make it to the Throne of Four Winds to take on Al'akir himself.
The lore is very sparse on the bosses of the dungeon. The first boss, Grand Vizier Ertan is a standard sentry, telling you that you're not welcome in the Skywall. The last boss, Asaad, Caliph of the Zephyrs seems to be a high ranking member of the elementals calling on Al'akir's aid during the fight. The title, Caliph, is an old title of Islamic leaders, and translates as successor. This fits with the Arabic theme that Blizzard has gone with for the denizens of the Skywall. Asaad is classified as a Djinni or Djinn, which are akin to genies. The middle boss of the dungeon is a dragon named Altairus. Altair means the flying one, or bird of prey in Arabic. Altairus drops Reins of the Dragon of the North Wind and starts the fight facing North. It makes sense that Al'akir would have flying creatures in his armies, as well as the many elementals.
Vortex Pinnacle introduces us to the Skwall, the armies of Al'akir, and the danger the pose to the land of Uldum and the rest of the world. When you go in to the instance, take some time to look around. It's actually quite beautiful.