If you are new to the study of insurance law, you may be confused by references to "first party" claims and "third party" claims. Who are these people, and what happened to the "second party"? These terms derive from reference to the insurance policy as a contract.
There are two parties to the insurance contract: the insured and the insurance company. By custom and practice, the insured is universally referred to as the "first party". The insurance company is the "second party" but for some unexplained reason, it is seldom if ever referred to in this manner. A "third party" is a stranger to the policy: that is, someone who is neither an insured or the insurer.
A first-party claim is one which must be paid directly to the insured. . A claim for property damage under a homeowners policy is an example of a first party claim: the insured has suffered a loss of his own property and, if covered, the insurance company is required to pay him directly for it. Coverage that provides such benefits is usually referred to as "first party coverage".
A third party claim is one that involves damage or harm to a third party (i.e., someone other than the insured). This is usually if not always a liability claim. If and when such a claim is settled, money will be paid to the claimant (the third party) rather than to the insured. A typical example of a third party claim is a lawsuit against an insured driver who negligently caused an auto collision. Coverage that protects an insured from exposure to liability in this manner is called "third party coverage".