After Ysgramor and his followers settled in Skyrim during the Merethic Era, they brought their native Atmoran religion with them. Known as the Dragon Cult, this faith worshipped numerous animal totems, namely the hawk, wolf, snake, moth, owl, whale, bear, fox and most importantly the dragon, as avatars of the gods. It is believed these totems were in fact early Atmoran interpretations of the divines.
The Atmorans regarded the Dragon as head of the pantheon, and considering Dragons existed in vast numbers across Tamriel and Atmora, it would eventually change into outright worship of living Dragons, Alduin being chief among them.
Dragons themselves were only too happy to encourage this practice. They believed that as children of Akatosh, they were naturally superior to both man and mer.  One of their core beliefs was that power equalled truth. The fact that they held immense power over mortals led them to the conclusion that this itself was the ultimate truth. This gave them the justification in their minds that their rule over mortals was only natural. 
Dragons embraced their role as god-kings over men, but rather than deal with the actual ruling itself, they granted small amounts of power to dragon priests in exchange for absolute obedience. In turn, the priests ruled men as equals to the kings. The priests set down laws and codes of living that kept peace between Dragons and men, but to do so they demanded tribute. Their system of rule was however corrupted and the priests began to rule with an iron fist, making slaves of the rest of the population.
Alduin's peers considered him the most acclaimed creation of Akatosh. Alduin basked in arrogance at these accolades. In favor of conquering Mundus for himself and his fellow Dragons, he forsook his "proper role" as World-Eater. 
Eventually man rebelled against the great crueltly of Alduin and the Dragons and the Dragon War began. At first, mankind was woefully outmatched, and was easily defeated by the Dragons and their voice.
Kyne intervened, and sent Paarthurnax to assist mankind. Paarthurnax, originally the first lieutenant of Alduin, betrayed his former master and taught the power of the voice to mankind, creating the first Tongues.
Mankind created a shout known as Dragonrend, built on the hatred of the Dragon's tyranny and oppression. Its use forces the concept of mortality onto the Dragon, something that is incomprehensible to an immortal creature, and temporarily stuns the creature.
The war reached it's climax when the ancient Nord heroes, Hakon One-Eye, Felldir the Old and Gormlaith Golden-Hilt, fought Alduin at a battle at the summit of Throat of the World. After Gormlaith was killed and Hakon was severely wounded, Felldir used an Elder Scroll to banish Alduin, however, this victory was only temporary, as he would re-appear in the Fourth Era.
The surviving dragon priests were overthrown. The survivors of the dragon cult adapted and went into hiding all across Skyrim. They entombed the remains of the dragons that died during the war within dragon mounds with the belief that Alduin would one day return and resurrect the faithful. However, other sects within the cult believed only those who ascended to the priesthood would be granted a second life.