I'll save you 23 minutes of your life that you'll never get back and tell you the short answer: Dawkins thinks that we are here in order to understand the universe. That is humanity's purpose. Now, my cynical side says: "Just like a scientist to think that humanity's purpose is science." But who knows, he may be right.
Me? I don't know if there is a larger purpose for humanity. If there is some great, cosmic reason we are here, it may well be too large for our limited human brains to grasp. And, much too often I think, the idea that there's some great, over-riding purpose for humanity is latched onto by unstable humans, who then twist it towards poor ends. For my money, I would say it's much safer in the long run to start people out by telling them: "There are certain principles pretty much everyone mostly agrees on - those are A, B and C. We don't know if these are absolute certainties, but they've worked pretty well so far. Beyond those extreme generalities, however, you're just going to have to take responsibility for your own morality. Keep in mind that this will require you to be able to think for yourself, and to make your own decisions. Or, you can just join the nearest woo-woo cult and spend your entire life without ever making up your own mind about anything, just obeying great leader. Your choice - have at it."