You start the game in Old Russia, Earth... dead, you are then brought back to life by a small robot called a Ghost. You must then escape the fallen, an alien race whose mission is to destroy the Guardian. You later find an old ship, and after shooting some aliens your ghost fixes the ship and you fly to The Last City where you then meet with other players around the world.
Destiny is a really great game, and even though I'm not getting it I had played the beta and had much fun doing so.