"Those who came before" once ruled over the earth with a highly advanced civilization, with many technological wonders, including the Pieces of Eden, which are made to work with their physiology. Through selective breeding, they made humans to be a docile and numerous workforce made in the First Civilization's image. Their minds could be affected by the Pieces of Eden, but they could not use them themselves. Eventually, humans rebelled against their creators, sparking war between the two groups, which blinded them to a greater threat. That threat was the sun itself, which - for lack of better non-technical phrasing - lashes out at the Earth every few thousand years. Caught unawares, the Earth was besot with a global disaster which practically destroyed the First Civilization.
Some vestiges remained, but "those who came before" were on the brink of extinction. Humanity was spared a similar fate by virtue of its susbstantially larger population. Putting aside their differences, the two groups worked together to ensure a similar fate would not befall their descendents through the creation of several 'vaults' that would both warn those that came after them and - hopefully - provide the key to protecting the world from the next solar disaster. Those remaining from the First Civilization also bred with humans, thereby creating bloodlines within humanity that could use the powers of the Pieces of Eden, and the abilities priorly unique to 'those who came before'. Everyone with 'Eagle Vision' is a descendent of at least one such union. It's worth noting here that Desmond is descended from many such bloodlines (Ezio is not descended from Altair, and Connor is likely of another bloodline), giving him an unusual concentration of First Civilization DNA.
Fast forward to the times of the games, and this history is lost to everyone. By modern times, both the Assassins and Templars are aware of 'those who came before' but not the nature of their extinction. It was not until the end of Assassin's Creed Revelations that the Assassins became fully aware of the gravity of the situation before them. By all indications, the Templars remain in the dark about it, with their current plans seeming to focus on launching a Piece of Eden into space in an attempt to take control over the planet in one fell swoop.
