Accreditation is important because it helps determine if an institution meets or exceeds minimum standards of quality and helps students determine acceptable institutions for enrollments.

Some universities claim that they are Approved or Registered in a particular state. This does not mean that they accredited but that they can operate as a business in that state.

In the US to be an Accredited university such university must be accredited by one of the Regionally Accrediting Organisations which are the following:

• Accrediting Commission for Community and Junior Colleges (ACCJC) Western Association of Schools and Colleges
• Higher Learning Commission (HLC)
• Middle States Commission on Higher Education (MSCHE)
• New England Commission of Higher Education (NECHE)
• Northwest Commission on Colleges and Universities (NWCCU)
• Southern Association of Colleges and Schools Commission on Colleges (SACSCOC)
• WASC Senior College and University Commission (WSCUC)

Generally speaking, if a US university is not accredited by one of the above accrediting organizations then is not considered accredited.

Examples of accredited universities:

Columbia University: Columbia is accredited by the Middle States Commission on Higher Education, one of six regional higher education accrediting agencies in the United States https://provost.columbia.edu/content/accreditation

University of Texas: Accreditation. The university is accredited by the Southern Association of Colleges and Schools Commission on Colleges to award baccalaureate, professional, masters, and doctorate degrees. https://provost.utexas.edu/sai

University of California: Each University of California campus is accredited by the WASC Senior College and University Commission (WSCUC). https://www.ucop.edu/institutional-research-academic-planning/content-analysis/academic-planning/accreditation.html

What Is A Diploma Mill

A diploma mill (also known as a degree mill) is an organization that awards academic degrees and diplomas with substandard or no academic study and without academic approval by officially recognized educational accrediting bodies or qualified government agencies.  https://en.wikipedia.org/wiki/Diploma_mills_in_the_United_States

How to Spot a Non-Accredited University

Typically such universities instead of listing one of the above regionally accrediting agencies they will mention that they are Approved or Licensed or they are authorised etc. They will not simply state that we are accredited by such and such Regionally Accredited Agency as per above examples. 

Some US universities delivering online degrees are claiming to be licensed under the Degree-Granting Institution Rules of a specific state and not under one of the Regionally Accrediting Bodies. The issue is that states do not accredit universities and they do not offer state accreditation. States provide an approval for such an operation to operate as a business. Specific programs still need to be accredited by one of the regionally accredited bodies if such programs are to be considered accredited.