Hyperpower is a neologism created by the French to denote a power that not only has no rival, but is orders of magnitude greater than its next closest rival. This term was created specifically to refer to the position of the United States after the end of the Cold War (when the US and the Soviet Union were referred to as superpowers, leaving the terms megapower, ultrapower etc. still to be coined). It has also been used (retroactively for analogous purposes) to describe the likes of the Roman Empire and the British Empire.
While neoconservatives hoped to harness the US's status as a hyperpower to change the world through the promotion of democracy and preemptive war, it appears they may have doomed the US to lose the status instead by pursuing unilateral and insular policies.