Third-party administrators (TPA) are essentially companies that function as intermediaries between the insurers and the insured.
Health insurers generally outsource the process of accepting intimations, approving cashless claims and settlement and disbursement of claims to TPAs, who issue identity cards to policyholders which need to be submitted to the hospital from where the policyholder wants to make a cashless claim. TPAs have a bigger role to play at the time of filing claims—you will first have to inform your TPA who will direct you to a hospital with which it has a tie up. Once this is done, the hospital will get an authorisation letter from the TPA following which all your bills will be sent to the TPA. The TPA forwards your bills and other documents to the insurer for your claim to be processed.
Note that if you choose to go to a hospital which does not have a tie-up with the TPA, you won’t be able to make a cashless claim but your expenses will get reimbursed by the insurer. However, you could still get the claim processed by the TPA.