The Titans are, if you strip all the cosmic power and grandeur away, meddlers. They go from world to world and change those worlds to their liking, whether or not the current inhabitants want them to, and Azeroth is no exception. When the Titans arrived, they found the world a seething battleground for raging elementals who fought for the amusement of ancient unfathomable entities called today by the sobriquet 'The Old Gods'. Entities like C'thun and Yogg-Saron are an example of the true lords of Azeroth. The quoted text at the bottom of this page gives you an idea of how the Titans wrested control of Azeroth away from them and sealed them in prisons beneath the planet's surface. With the elementals banished to other planes and the Old Gods trapped, the Titans then rearranged Azeroth to their liking.
However, since the Titans re-ordering of the world is imposed, they require shepherds to maintain it. While the Titanic Watchers of Ulduar were set to maintain Yogg-Saron's prison, they were not entrusted with the maintenance of the world itself, possibly because they were not of it. From Galakrond's offspring, known today as proto-dragons, the Titans shaped flights of dragons to the vital (to them, at least) task of preserving their hard-fought order. Black, Blue, Green, and Bronze were each given dominion over a key aspect of the Titan's new world. And to Alexstrasza, the Red Dragonqueen, was given control over Life itself. This was the birth of the Red Dragonflight, perhaps the most beneficent grounp of enormous fire breathing reptiles one could hope to encounter. They are dragons, however, so don't take them for granted.