Most graduate schools require an undergraduate degree from an accredited university. Accreditation is the quality assurance process that educational institutions undergo. Accreditation is also the term applied to the credentials that an institution or program earns after the periodic reviews conducted by peers and member-based associations.
This system of self-regulation ensures that you're getting a quality education and encourages any necessary improvement in the school's programs. Accreditation also helps protect you from diploma mills and accreditation mills — two types of providers that grant questionable (or, at worst, invalid) credentials. Accreditation mills pump out credentials to whoever pays them their fee and lend an air of authenticity to a bogus program or "college."
Recognized accrediting agencies (these are the ones you want) are governed by the U.S. Department of Education and the Council for Higher Education Accreditation (CHEA). These agencies can be regional, national, or specialized — and the accreditation should be listed on the school's Web site and in the school's recruitment materials. Contact these agencies directly with your questions about the school in question.