The basic idea is that in the event of an Internet catastrophe, the DNSSEC (domain name system security) could be damaged or compromised and we'd be left without a way to verify if a URL is pointing to the correct website. That's when the holders of these smart cards would be called into action:
A minimum of five of the seven keyholders – one each from Britain, the U.S., Burkina Faso, Trinidad and Tobago, Canada, China, and the Czech Republic – would have to converge at a U.S. base with their keys to restart the system and connect everything once again.
A minimum of five people is needed because each of the smart cards contains only a fraction of the recovery key necessary to set things right again. This means that no single person will hold all the power to resetting our little cyber world. [BBC via PopSci]"