Emergency communication is the first reason the FCC gives for the amateur service's existence. In practice it means trained volunteers with their own equipment who can move accurate information when cellular, internet and public-safety systems are saturated or destroyed.
It also means training, drills and paperwork long before anything happens. The operators who are useful during an activation are the ones who were on the weekly net all year.
Related topics: nets for the weekly practice that makes it work, clubs and community for the groups that organize it, and the station for power and portable equipment.