Did you play the first game? If you didn't, Desmond's part would probably make more sense if you did. Desmond was born into a modern day brotherhood of assassins but he left them when he was a teenager. Abstergo, the modern day templars (the bad guys) captured Desmond and put him in the animus, which is a machine that is able to access ancestral memories that are locked away in what real life scientists call 'Junk DNA'. He was forced to relive the memories of Altair, so that the Templars could locate the piece of Eden, an all powerful artifact that was created by Those Who Came Before, a race of beings that were mysteriously wiped out before the beginning of human civilisation. When Lucy helps Desmond escape, she takes him to the modern day assassins and he is put into a new animus. He relives the memories of Ezio so that he can find out more about the piece of Eden. The Bleeding Effect also starts to affect Desmond and he starts to acquire the skills of his ancestors. That's Desmond's story up to Assassin's Creed II but Ezio has a completely different story as he is in a different place in time.