By spreading risk, an individual insurance company can take on clients whose coverage would be too great of a burden for the single insurance company to handle alone. When reinsurance occurs, the premium paid by the insured is typically shared by all of the insurance companies involved (the one I am working with is 80% reinsurer and 20% the cedent).
If one company assumes the risk on its own, the cost could bankrupt or financially ruin the insurance company and possibly not cover the loss for the original company that paid the insurance premium.
For example, consider a massive hurricane that makes landfall in Florida and causes billions of dollars in damage. If one company sold all the homeowners insurance, the chance of it being able to cover the losses would be unlikely. Instead, the retail insurance company spreads parts of the coverage to other insurance companies (reinsurance), thereby spreading the cost of risk among many insurance companies.
Reinsurance and insurance regulations vary state by state. California is very regulated.