Okay, it is revealed to Ezio/Desmond (by Minerva) that the god/gods that human beings worship weren't really gods at all, but extraordinarily powerful ancient beings. They created the progenitors of human beings (in their image), all embedded with a mind control device inside their brains. Adam and Eve are created, and they are the first Assassins (though they don't know it yet). Adam and Eve rebel against their masters, steal the Apple (A piece of Eden) and escape from the "garden" of Eden. This begins a war between the god-like Ancients and the beings that came before us human beings. Some sort of cataclysm happens, and these god-like ancients are destroyed (the ending suggests that this will happen again in the future).
The Pieces of Eden (the apple, the staff and other artifacts) possess unique powers. Wars are fought over these items by the Greeks, Romans, etc. Fast forward through time a bit, and Cain kills Abel for possession of a Piece of Eden. Cain becomes the first Templar. Fast forward again through time and famous figures and events of our history are shaped by these artifacts from Eden. Jesus Christ, Nikola Tesla, Thomas Edison, Houdini, George Washington, Queen Elizabeth I, Genghis Khan, Napoleon, Hitler, Teddy Roosevelt, John F. Kennedy, Gandhi, etc etc.
All of these figures in history are connected somehow with the Pieces of Eden. I'm not sure which were Templars and which were Assassin's, but it's suggested that wars are fought over these artifacts, and lives were taken.
Altair, Ezio, Subject 16, and Desmond are direct descendants of Adam and Eve. I thought about it, and it would explain how Eagle Vision works and how Assassin's have such incredible agility. In the Subject 16 video you see Adam and Eve perform awesome leaps and jumps that are very similar to what Assassin's are capable of.