Essentially, shortly after Medivh opened the Dark Portal, at the end of the Black Morass instance, the orcs moved into Azeroth, and established their home there, around the Dark Portal, ravaging the land and causing it to resemble their homeland, in the Hellfire Peninsula, on the other side of the portal.
At the end of the events of Warcraft 2's main campaign, the mage Khadgar annihilates the Portal utterly, although it was already located inside a crater. Likely, the magical discharge caused the after-effects we see, today. Also, as per the WC2 expansion, the Portal was not completely destroyed; other heroes, many of whom are seen in Outland, including Danath Trollbane, Alleria, and, of course, Khadgar, journeyed to the other side, to destroy the Portal from that side, an event which fractured the planet of Draenor, turning it into the floating series of islands we see today, in Outland.
Videos of the ending of WC2 and WC2 expansion: Khadgar destroying the Dark Portal Khadgar destorying the Dark Portal in Draenor, using the Skull of Guldan