When a school in the United States is accredited, it means that it has passed a set of criteria stipulated by an accreditation agency. The U.S. Department of Education maintains a list of accreditation organizations that meet federal standards and a list of schools that have been accredited by those groups. So, for a school to be accredited in the U.S., it must have received accreditation through a federally recognized organization. Prospective students can check a school's accreditation by going to the U.S. Department of Education database at Ed.gov.
Accreditation is important because it ensures the quality of the education a student will receive at an institution. If there were no criteria in place to judge the validity of a school's educational program, students would have no way to determine which schools were worthwhile and trustworthy. With accreditation, there are some across-the-board standards applied to all schools, and students know that they will receive a quality education. Students need a way to trust that the degree they are working toward will be valuable upon graduation.
If students attend a school that isn't accredited, there may be a number of results. They may have a great educational experience at that institution and learn things that will be valuable to their future. However, students should know that any degrees earned will be unaccredited as well. This means that students will not be able to use those degrees to apply to graduate school. It also means that they will not be able to transfer those credits to an accredited school to use toward accredited degrees. Also, most employers either require or prefer a degree from an accredited institution. So, an unaccredited degree will most likely be of no value in a job search. Students who are interested in going to an unaccredited school should do so for the experience, not the degree.