If a certificate asks you to trust an assessor, a further question appears: who has examined the assessor? Accreditation addresses that second level. It recognizes an assessment body's competence within a defined scope.
In the certification setting, an accreditation body evaluates a certification body. This is different from certifying the final product or awarding a qualification to an individual worker. The object of scrutiny has moved up one level.
Imagine several testing organizations offering apparently similar assurances. A purchaser may lack the expertise to compare their methods, independence, and competence. Accreditation can provide a common reference, reducing the need for every purchaser to investigate each assessor alone.
It remains important to follow the scope. An organization recognized for one class of assessment does not thereby become qualified to assess everything. Nor does adding another institution remove the possibility of errors or conflicts of interest.
The social mechanism is a chain of delegated scrutiny. Each layer makes specialized checking usable by people who cannot perform it themselves. That chain is helpful when its claims are understandable and verifiable; it becomes confusing when all the different badges are treated as interchangeable signs of general excellence.