The Collaborative International Dictionary of English v.0.48:

Reinsurance \Re`in*sur"ance\ (-sh?r"ans), n.
   1. Insurance a second time or again; renewed insurance.
      [1913 Webster]

   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.
      [1913 Webster]

WordNet (r) 3.0 (2006):

reinsurance
    n 1: 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"

Bouvier's Law Dictionary, Revised 6th Ed (1856):

RE-INSURANCE, mar. contr. An insurance made by a former insurer, his
executors, administrators, or assigns, to protect himself and his estate
from a risk to which they were liable by the first insurance.
     2. It differs from a double insurance (q.v.) in this, that in the
latter cases, the insured makes two insurances on the same risk and the same
interest.
     3. The insurer on a re-insurance is answerable only to the party whom
he has insured, and not to the original insured, who can have no remedy
against him in case of loss, even though the original insurer become
insolvent, because there is no privity of contract between them and the
original insured. 3 Kent, Com. 227; Park. on Ins. c. 15, p. 276; Marsh. Ins.
B. 1, c. 4, s. 4