In the U.S., the government does not accredit schools. However, the USDE is in the business of recognizing the associations which do accredit schools. Such recognition carries significant meaning. In a few countries of the world, existing Universities of exceptional standing may, with approval of the national government, accredit other smaller or less recognized schools. There are some countries where accreditation or its equivalent is required, but usually not.
Accreditation is most often voluntary.
Accreditation in the U.S. is voluntary, though in some states it is difficult to operate without it. However, this is not the same as accreditation. Many schools in the U.S. are recognized as top-quality institutions with high academic standards and yet have, for various reasons, elected to not seek accreditation. Of course, all schools in the U.S. seeking recognized accreditation must first operate as an unaccredited school and provide sufficient proof of institutional credibility prior to applying. Practically speaking, all accredited schools in the U.S. were, at one time, unaccredited.