Reinsurance is not as complicated as one might think. When an individual purchases an insurance policy, a premium is paid by the individual, and the insurance company pays the claims. An insurance company wants to make sure they bring in enough premium to cover the cost of claims plus operating costs and hopefully have a decent profit left over.
One way that an insurance company can lose money on a policy is if the insured experiences an extreme large loss. If a very large loss occurs, the insurance company cannot make enough money to cover operating costs for the policy. If many policies experience large losses, then the company is at risk of losing money overall.
Enter reinsurance. To hedge against the risk of large losses, an insurance company pays a premium to another insurance company to cover the costs of large claims. When a claim cost exceeds the reinsurance amount, the reinsurer pays the claim. This allows the original insurer to experience greater financial stability since they know the maximum amount they will pay on a policy. The reinsurance premium will often be larger than the annual cost of large claims, but companies are willing to pay a fixed cost in exchange for shifting the risk to the reinsurer.