Source : Webster's Revised Unabridged Dictionary (1913)

Reinsurance \Re`in*sur"ance\ (-sh?r"ans), n.
   1. Insurance a second time or again; renewed insurance.

   2. A contract by which an insurer is insured wholly or in
      part against the risk he has incurred in insuring somebody
      else. See {Reassurance}.

Source : WordNet®

reinsurance
     n : sharing the risk by insurance companies; part or all of the
         insurer's risk is assumed by other companies in return
         for part of the premium paid by the insured; "reinsurance
         enables a client to get coverage that would be too great
         for any one company to assume"