Klaatu's warning concerns global warming: Earth is too valuable a planet to let humans destroy it, so the solution is to annihilate the human race entirely. Klaatu is unconvinced that humans can change their ways, even after meeting another scientist (John Cleese) and a fellow alien who's been living on Earth for over 70 years and has grown fond of our planet, both of whom try to change his mind.
After a series of alien spheres depart carrying different species inhabiting Earth, a captive Gort transforms into a massive cloud of insects which proceed to slowly consume everything they come across. After watching Helen and her adoptive son (Jaden Smith) bond over the boy's dead father, Klaatu realizes the human race is capable of changing their hostile ways and ends the planet's destruction by approaching the giant sphere he arrived in.
A resulting shockwave shuts down all technology on Earth, hence the film's title.