Every university, real or fake, is accredited by someone, but the three that most matter for MBAs are AASCB, AMBA and EQUIS. This is explained well: Take a look at http://find-mba.com/mba-faq/mba-accreditation-why-is-it-important It explains the three respected accreditations. Good MBAs have one or more. I also wrote a nice analysis: Why international accreditation matters http://www.find-mba.com/board/41224

Below that, for US universities, are regional and national accreditation. The former is better than the latter. One of the least useful nationally-accredited accreditation bodies is ACICS, which mostly accredits low-quality for-profit colleges. Despite being over 100 years old, it has gone through a period of decline and lost recognition by the CHEA earlier this year. https://www.goodcall.com/news/students-schools-overseen-troubled-accrediting-agency-acics-options-07848 It is now a warning sign to be accredited by that body. Many of its members are in deep trouble, with one closing this month http://www.educationdive.com/news/acics-fallout-forces-non-profit-college-closure-in-colorado/431441/

I've never even heard of most of the schools that ACICS accredits. For example, they have names like "California University of Management and Sciences," "Charter College," and "Herguan University."