Warlords of Draenor didn't launch with flying mounts, and for a long time Blizzard didn't intend to implement them. After months of consternation among World of Warcraft devotees though, Blizzard announced in June that, yeah, they'd allow players to fly in Draenor after all. Now, with tomorrow's 6.2.2 patch, the functionality will finally roll out.
Not without conditions though: you'll need to put a few weeks into the game if you want to unlock mounts, though most players have probably already met the requirements. When I spoke to lead game designer Ion Hazzikostas in June he put it this way:
"The solution was to preserve our original design goal of ensuring players are exploring the world and experiencing it from the ground, and getting to appreciate its scope and its size and engaging the gameplay aspects of exploration and mystery. Then, once they’ve done that, there’s no reason not to allow them to fly and navigate in all dimensions throughout the world, and also unlock that ability for their alts."
The video embedded below (courtesy of Wowhead) does a good job of outlining all the work you'll need to do in order to unlock the Pathfinder achievement, which itself unlocks access to flying mounts.