Organizations which certify third parties against many official standards are themselves formally accredited by the standards bodies, hence they are sometimes known as "accredited certification bodies". The accreditation process ensures that their certification practices are acceptable i.e. they are competent to test and certify third parties, behave ethically, employ suitable quality assurance and other measures etc.
Examples include accredited test laboratories and certification specialists that are permitted to issue official certificates of compliance with physical, chemical, forensic, quality, security or other standards.
Without accreditation, anyone would be able to issue certificates and bad practices or incompetence might discredit the certification process as a whole. The flip side, of course, is that accreditation and formal processes incur additional costs.