By definition, the word "accredit" means to authorize, endorse and officially approve of. What ordination is to a minister, accreditation is to a school.  Accreditation is a group process by which schools voluntarily agree to participate in a set of established standards in order to encourage quality education.

Schools are not legally required to become accredited, but it is a very desirable standing. Accredited status means a school has voluntarily undergone a comprehensive examination to determine that it operates at a worthy level of performance.

National Accrediting Agency of Private Theological Institutions, in accordance with the inspired teaching of the Bible, has chosen not to seek endorsement from either the EAES or CHEA. The following quote is taken from the web site of the Council for Higher Education Accreditation (CHEA).
There are accrediting organizations that may not be recognized but are not accreditation mills. For example, the accreditor may be seeking recognition, but the process is not complete. Or the accreditor does not meet the requirements of CHEA or USDE for reasons that do not relate to quality."
The following quote is from the United States Department of Education:

"It should be noted that some institutions have chosen not to participate in the federal student aid program and therefore do not have to be approved by an accrediting agency recognized by the Department. While these institutions do not appear on the Department's list, they may be legitimate schools."
This quote from the former executive director of the Association for Biblical Higher Education (an accrediting agency recognized by the United States Department of Education), stated as follows:

"There are hundreds of Bible Colleges and Seminaries in the United States and Canada that are offering good solid theological training, yet they are not accredited." 

                        SEPARATION OF CHURCH AND STATE: 

There is secular education and there is religious education. Secular schools seek secular education, and sacred schools receive sacred accreditation—each by their own peers. Religious institutions need no secular accreditation unless they offer secular degrees and are required to have such government oversight in order to grant their degrees.
Secular accreditation associations in turn are recognized by governmental agencies. They trace their authority back to the capitol of a country, like Washington, D.C.
Religious accrediting associations are recognized by the Church of our Lord Jesus Christ, which has no supreme central office on earth. Our authority is derived directly from Heaven. However, because of unscrupulous practices resulting in "diploma mills" and "accreditation mills", reputable theological institutions would be wise to obtain reputable accreditation.
Civil and religious interests are different and have separate realms of jurisdiction. The State is not superior to the Church. The Church need not wait for approval from the secular world. Civil agencies should not be dictating standards of Christian education, any more than a police officer should be directing the worship of God.
Theological Seminaries should not be accredited by accrediting associations that are "recognized" by an agency of the federal government, because it is contrary to the Biblical principle of "Separation of Church and State," indicated by Christ when He said, "...Render unto Caesar the things that are Caesar's, and to God the things that are God's..." (Mark 12:17).
What business does a Christian educator have in going to the world of unbelievers for recognition and acknowledge-ment when II Cor. 6:14 clearly tells us, "Be ye not unequally yoked together with unbelievers; for what fellowship does righteousness have with unrighteousness?"
There is no such thing as Federal or State accreditation of a Bible school, for civil government has no authority to regulate religious training or what certificates we issue for it. This is an issue of separation of church and state.

Civil authorities must never officially endorse or disapprove directly. On the other hand, there are some who discount a Christian school and reject their accrediting or indirectly the beliefs and practices of churches or their Bible schools.
A casual survey of church history shows that such linkage with Caesar eventually leads to infringement upon conscience, bondage, and corruption. Therefore, to be accredited by any agency, which in turn is supervised by the U.S. Department of H.E.W. would, to some degree, be a compromise of the separation principle and constitute "friendship with the world” condemned as "adultery” by James 4:4.

NAAPTI - National Accrediting Agency

A legitimate, valuable, affordable and reputable accrediting agency