3rd party certification is independent verification that a product or service has the expected performance. Most certification bodies require an initial assessment, which for products will include a review of test evidence, followed by periodic inspections and audit tests to verify the ongoing performance.
Other types of certification include 1st party, which would be a statement of compliance by the provider of the service, and 2nd party, which would be certification by a party who is connected in some way to the supplier of the service (e.g. a component supplier).
3rd party certification still requires the provider of the service to take responsibility for what they supply as the certification is based on verification at periodic intervals. 3rd party certification is therefore not a guarantee of the performance of the product or service that is covered.