The Throne of the Tides is located in Vashj'ir. More specifically in the Abyssal Maw within a large, hard to miss, whirlpool. It's important to note that while the instance is available immediately at level 80 you don't have a lore reason to go there until you've completed the entirety of Vashj'ir. So much of this post will be a spoiler for what you experience while questing in that zone. If you have quested in that zone, hopefully this will sum up what you experienced and fill in anything you may have missed. Again, spoilers for Vashj'ir if you have not completed the zone.
If you get the quest from your major city to Vashj'ir, you'll be put on a boat and shipped off over seas to get there. But it doesn't take long before you're attacked by a giant squid. That's Ozumat. Remember him, you'll be seeing him again. Lost at sea, you're rescued by the Earthen Ring, specifically by a shaman named Erunak Stonespeaker. He'll set you and your buddies straight, teach you to breath and walk under water, and put you on the path to go through the rest of the zone. After a few more quests, you'll be attacked by a force of Naga and get the general idea that the Naga are after something here and are building an army and taking prisoners to accomplish that something.
A little later on, Erunak will have you go on a sort of vision quest in which you act out events that happened sometime in the past as a Naga Battlemaiden under the command of Lady Naz'Jar. Lady Naz'Jar and her battlemaidens are fighting against the Vry'kul who have taken up residence in the ruined city of Vashj'ir. It is here that you begin to learn of the Naga's intentions. After taking back the city of Vashj'ir, the Naga intend to mount an attack upon
Neptulon, Elemental Lord of the Water. This is where things get interesting.
Neptulon is one of the four elemental lords, along with
Ragnaros,
Therazane, and
Al'akir, all of which make appearances in Cataclysm. We know that Ragnaros and Al'Akir have sided with Deathwing, whereas Therazane becomes friendly with players during the events in
Deepholm. It is well known that the Naga were once Night Elves who were drowned after the events of the Sundering 10,000 years ago, including Queen Azshara herself, and it was speculated that Neptulon, under the Old Gods influence had initiated that transformation. But with the events of Cataclysm and Vashj'ir, it seems more apparent that the Naga were transformed directly by the Old Gods, and now they seek to overthrow Neptulon and take his place as rulers of the water.
So all of this culminates in an epic battle where you, Erunak, and Alliance and Horde forces face off against the Naga as they attempt to destroy Neptulon. The Naga, with the aid of faceless ones and Ozumat (the squid who shipwrecked you) are able to push Neptulon down to the Throne of Tides through the Abyssal Maw. Erunak is captured and taken down there as well. Lady Naz'jar, who spearheaded the Naga attack on Neptulon now has him imprisoned in his own throne room, and it's up to you to free him and make sure the realm of water stays under control of the elements and not the Naga.
So now we finally have an understanding of what all of these people are doing within the Throne of the Tides.
Lady Naz'Jar is the first boss, and was the one who organized the Naga attack upon Vashj'ir and Neptulon. While she wasn't able to destroy him, she was able to push him back to the Throne of the Tides. Thankfully you'll be able to get rid of her before she's able to cause further damage.
Commander Ulthok, The Festering Prince is a faceless one, which further seems to implicate the Old Gods and the Naga are in cahoots. He appears after you get rid of Lady Naz'Jar, attempting to stop you from getting any further than you already have.
You find Erunak Stonespeaker within, but he's being mind controlled by Mindbender Ghur'sha, who also happens to be attached to Erunak's head. Your goal here is to rescue Erunak and hopefully not have to kill him in order to get rid of Ghur'sha.
With Lady Naz'Jar defeated, Erunak rescued, and all other obstacles removed, your last task is to rescue Neptulon who has been weakened and trapped in the throne room. It's important that you free him because the Naga's pet squid, Ozumat, is out to finish the job he started at the Abyssal Maw. With a little help from Neptulon, you should be able to get rid of Ozumat and ensure that Neptulon remembers what you did for him when the time comes to fight Ragnaros in Patch 4.1.
I wish that I had been able to finish Vashj'ir before I did Throne of the Tides for the first time. The design seems a bit wonky in that you can easily finish Vashj'ir and out level the instance before you even know about it, or have the quests for it. And it's a shame too, since the way the story of Vashj'ir culminates in a huge battle and a dungeon where you assist the Tidehunter in a fight against a giant squid is pretty epic. When I went in for the first time, I had no idea who Naz'JarVasj'ir.