According to the site:
In "After Earth," one thousand years after cataclysmic events forced humanity's escape from Earth, Nova Prime has become mankind's new home. Legendary General Cypher Raige (played by Will Smith) returns from an extended tour of duty to his estranged family, ready to be a father to his 13-year-old son, Kitai (played by Jaden Smith). When an asteroid storm damages Cypher and Kitai's craft, they crash-land on a now unfamiliar and dangerous Earth. As his father lies dying in the cockpit, Kitai must trek across the hostile terrain to recover their rescue beacon. His whole life, Kitai has wanted nothing more than to be a soldier like his father. Today, he gets his chance.
So this video isn't really a trailer per se, but more of a quick summary of events happening over a thousand years prior to the movie. The most implausible thing? That Facebook would be allowed to exist in a world-wide totalitarian state.