Reinsurance is business of insurers selling off insurance risk to others. It allows companies to spread the risk more evenly so that none are overexposed to individual events.
The idea of insurance is that an individual spread his own risk around by buying insurance so that the risk is shared among all of the world so one is not overexposed to an event such as a fire or a car accident that might potentially wipe you out.
Reinsurance is basically insurance for insurance companies. They sell of portions of their risk to reinsurers who then assume the risk of the policy, but also collect a portion of the premiums.
This system is what allows insurers to not be overexposed to a specific calamity, or even a specific region of the world.