The rest of Azeroth... didn't really enjoy that. Like, at all. It actually kind of sucked. So the people of Azeroth rallied behind Malfurion Stormrage, Tyrande Whisperwind and the demigod Cenarius. Unfortunately, Illidan is a jerk and a sellout, and warned Azshara that they were coming to stop the summoning of Sargeras. The ensuing battle had many, many casualties thanks to the extra preparation time Illidan gave Azshara, but Malfurion eventually met the Queen in combat. The battle threw the magics of Sargeras' summoning out of control and triggered what would be the first in a long, long history of Night Elves causing catastrophic, world-changing explosions.
Illidan, endlessly watching out for his own hide, managed to scoop up and preserve a number of vials of water from the Well of Eternity before it exploded and sundered the world in twain. One vial was used to create a new Well of Eternity(and thus a new conduit for the Legion) on Mount Hyjal, which landed him in prison under Maiev's watchful eye. The others were scattered and hidden by Illidan beforehand for one reason or another. Dath'Remar Sunstrider*, one of the Highborne who opposed Queen Azshara, was present when Illidan created the new Well. Though he opposed the Legion, the return of the Arcane to the Kaldorei was something he supported, seeing it as one of the Elves' greatest strengths. He fought tooth and nail to return the Arcane to the now-Druidic Kaldorei society, but they'd have none of it.
Dath'Remar eventually accepted this and decided to leave the Night Elven lands entirely with the Highborne faithful to him. They loaded up in fancy ships and braved the newly formed Maelstrom to travel east, where they would found their own land. Dath'Remar Sunstrider, now the first of the Sunstrider Dynasty, founded Quel'Thalas in the northern regions of what are now the Eastern Kingdoms, the Tirisfal Glades. He also had something in his possession that would guarantee the survival of the Highborne: One of Illidan's Vials of Eternity.
The Sunwell was born, and with it came power unending. The Highborne's hunger for the arcane was sated, and they found themselves capable of altering the very land itself in any way that they wished. The climate, the wildlife, it was all theirs to control. Massive towers and runestones were erected to harness the Sunwell's power, channeling magical shields and defenses to protect their new home from invasion. This lasted about... oh, a few thousand years. Man, is that all? They should've hired a better architect.
Wars were fought with the nearby troll tribes, but nothing devastating ever struck the kingdom of Quel'Thalas. It held firm until the day Arthas Menethil and the Scourge looked their way. The Scourge, armed with a fresh batch of corpses from their recent parade through Lordaeron, struck hard and fast into the heart of the Elven kingdom, with the intent of using the Sunwell's waters to raise the necromancer Kel'thuzad from the dead. Prince Arthas reached the Well relatively easily, leaving a blighted scar straight through the kingdom and the capital city of Silvermoon, and plunged the Necromancer's remains into the waters. Kel'thuzad rose as a lich, and the waters of the Sunwell were twisted and blighted. The glorious magics of the Well became corrupt and terrible.
Though Arthas moved on, much of the Scourge remained in Quel'thalas, to finish off what remained of the High Elves. In a last ditch effort to save his people, Prince Kael'thas took a page out of Malfurion Stormrage's book and blew up the Sunwell, destroying the undead abominations. It proved successful, assuring the survival of the High Elves, now called 'Blood Elves,' but in the long term it was devastating to the people of Quel'thalas. Their reliance on the arcane ultimately led to the events depicted throughout Warcraft III: The Frozen Throne, and The Burning Crusade. Allison and I had a bit of a back and forth about this, so if you don't know the story of the Blood Elves during those periods, I recommend giving them a read.
Though the Sunwell was destroyed, the very essence of the Well remained. How? Who knows. For some reason, though, Krasus decided the best way to protect and preserve this essence was to disguise it as a hot chick and put it in a town a hop, skip and a jump away from Scourge territory in an attempt to hide it from the Scourge. O... kay. Sure, why not. Why didn't Krasus just put it somewhere safe, like with the Dragonflights? Who knows! Anyway, the essence of the Sunwell became known as Anveena Teague. A series of awkward events led to this magical construct falling in love with Kalecgos, a dragon. Dar'Khan Drathir, Betrayer of Quel'thalas, captured Anveena and attempted to siphon her power for his own use. He ultimately failed, and Anveena sought refuge in Silvermoon City, under the protection of Regent Lord Lor'themar Theron.
Everything we know from here is a lot of speculation and guesswork. We know that Kael'thas seeks to reignite the Sunwell using Anveena. The Fury of the Sunwell trailer also tells us that Kael'thas is repeating history, using the Well's power to summon the Legion's current Commander to Azeroth, attempting to regain the power Quel'thalas lost. Sunstrider Loyalists seem to have sold Anveena out and turned her over to their Prince, since last we knew she was safely in the hands of the Regent Lord, who we assumed was a benevolent leader. It is possible he simply underestimated the lengths Kael'thas would go to, and did not really expect Kil'jaeden to show up in his backyard. It's also possible Sunstrider Loyalists simply stole Anveena away in the night and took her to the plateau.
In summary: The Sunwell is a fountain of magic that exploded, then a dragon turned it into a hot chick, then another dragon fell in love with it, and now Kael'thas is using it to summon a bad guy. The end.
If you want to read further on the Sunwell before patch 2.4 hits, or even after, there's a ton of information out there for you. As much as it pains me to recommend anything written by Richard Knaak, the War of the Ancients trilogy will bring you up to speed on the Well of Eternity. Richard Knaak's Sunwell Trilogy manga will tell you the story of Anveena. Beyond that, most of your information will come from simply playing the games. Warcraft III and WCIII: The Frozen Throne will tell the beginning, WoW: The Burning Crusade will tell you the middle, and patch 2.4 will tell you the end. So go, game!
*Dath'Remar Sunstrider has a shrine in Eversong Woods dedicated to him and his sacrifice in battle against the Scourge. It's likely this is an error and it should be Kael'thas' father, Anasterian Sunstrider. As far as we know, High Elves are not immortal and DO age. If Dath'Remar Sunstrider were alive during the Third War, that would make him over 10,000 years old. Pretty good, for a mortal. Anasterian Sunstrider fought and died during the Third War, defending Quel'Thalas. This shrine should probably bear his name, not Dath'Remar.