Basically modern humans and neanderthals were bred by a more advanced and ancient form of humans (physically similar to AMH) we were all designed to have a naturally occurring fractal antennas in our brains that allowed them to mind control us to be used as slave/servants (humans) and soldiers (neanderthals). Some humans had a mutation (either naturally occurring, or a case of sleeping with the help which was also implied in the game, basically seraphim doing earthling hot chicks > flood recap) that made them immune to the mind control tech. There was a rebellion and a catastrophe (solar eruption) the ancients mostly have died out, some organizations know about them and some parts of the mind control tech have survived (pieces of eden in the game). The templars are after that tech to control the entire world, the assassins want to stop them.
PSA: That's pretty much spoiler free you can probably find a whole recap of the premise online.
[0] - the story of Biblical Deluge tells that part of the reason God had to sink the planet is that because angels descended from heaven and started breeding with people and corrupting them. If one believes in that story and is particularly imaginative, one had to ask just what level of technology did we have back then, after being 'corrupted' by what would be aliens?