The word 'privity' essentially means 'private'. In contract law, the phrase 'privity of contract' indicates that a contractual relationship is a private one, existing only between those persons who are a 'party' to the agreement, either because they have executed a deed or because they have provided consideration in support of an informal contract.
Under the 'doctrine of privity of contract' only the parties to an agreement have the right to enforce the contract: anyone who is not a party to a contract is described as a 'third party' and has no legal right to enforce the obligations created by that contract.