NAEYC is the National Association for the Education for Young Children. NAEYC accreditation is just an additional accreditation centers can get on top of state accreditation. NAEYC is a great organization, but it does cost extra. NAEYC has different standards as far as teacher/staff ratio, etc.
I worked at a NAEYC accredited center that was working so hard to fill all of the standards and requirements that I felt some things fell by the wayside and therefore the center suffered. I worked at a preschool that wasn't NAEYC accredited and they were fantastic. Aside from the teacher/staff ratio, having to create portfolios depicting all of the NAEYC standards, the paperwork etc I felt as if there really wasn't a big advantage either way.