In a short summary, Titans go around creating and shaping worlds according to the anti-chaos beliefs of the order of the Pantheon, the Burning Legion goes around destroying them.
Azeroth was rid off the Old Gods, created Dwarves from stone to shape the earth and Sea Giants to shape the sea, and then they created the Well of Eternity, which drew energies from the infinite Great Dark beyond the world to nourish all life. Before leaving, the Titans empowered 5 dragon aspects to safeguard their creation. The Well enhanced a primitive tribe of nocturnal humanoids; these would be known as the Night Elves.
The Night Elves' society was established, but Azshara and her loyal Highborne priests fell to an obsession about the Well's powers. Their reckless use of magic sent ripples of energy flying out and attracting the attention of Sargeras. They were so corrupted by magic that they immediately agreed to help him enter the planet once they were contacted.
While Sargeras was too big yet to pass, lesser Demons, like Infernals, Doom Guards and Felhounds, under the command of Mannoroth and Archimonde, made their way through the opened rift and broke in war with the Night Elves. Malfurion sought the help of his brother, Illidan, who was himself one of the Highborne, Tyrande, and Cenarius, who himself enlisted the aid of the Dragon Aspects. In a crucial battle, however, Neltharion, who renamed himself Deathwing afterwards, went mad.
Furion suspected that the Well was the gateway to the demons and convinced his group -- all except for Illidan, who broke from the crew and went to warn the Highborne of his brother's plan -- to strike Azshara's temple.
They were eventually successful, the Demons would be expelled from the world, and would later corrupt the Orcs on Draenor and get Gul'dan to open a pathway to Azeroth and engage in war with the Humans. By then, the Highborne, who continued to be addicted to magic even after Azshara's fall, had mocked the druids and unleashed a magical storm on Ashenvale, and had been thrown out of the lands due to that. They eventually settled on Lordaeron, their skin became lighter and they became High Elves. They were part of the Alliance who combated the Orcs during the Second War (WarCraft II) if you recall.
If you're looking into the entire story, here's
chapter 1: mythos.