Accreditation is a voluntary process by which primary and secondary schools, colleges, universities, and professional schools submit themselves to an comprehensive review process by an outside agency to ensure quality and institutional integrity. While there are a few quality Christian schools that don't seek regional accreditation for theological reasons, it remains the standard of quality within the United States.
Some schools have both regional and specialized accreditation.
If you select a school that only has specialized accreditation, be aware that your efforts may not be as accepted within academe. For better or worse, there are various levels of respect associated with the different accrediting agencies and the regional agencies are considered the standard. If you are pursuing a college degree through distance education then accreditation is a must. Many graduate programs and employers require an accredited degree as a prerequisite and simply discount unaccredited programs. I have received e-mail from people who spent much time and money working on an unaccredited degree, only to have it rejected by their school or employer.