Plain version: reinsurance is insurance for insurance companies. The insurer that sold your policy can buy its own protection in case the claims it owes grow too large.
Definition (Ins. Code §620): a contract of reinsurance is one by which an insurer procures a third person to insure it against loss or liability by reason of the original insurance. The buyer of reinsurance is always an insurer. A policyholder who buys a second policy on the same property is just carrying more insurance, not reinsurance.
Why insurers buy it:
Capacity: write larger policies than the insurer could safely carry alone.
Catastrophe protection: guard the insurer's financial position against very large losses.
Stability: make results steadier from one year to the next.
What it does not do (§623): the original insured has no interest in a contract of reinsurance. After a loss, the insured still looks to its own insurer, not to the reinsurer.