What is the difference between earning an accredited and non accredited degree ?
How important an issue is it ?
Are all legal degrees accredited ?
These answers depend upon what you mean by accreditation.
The term started in the United States where the State governments are responsible for licensing educational institutions and the Federal Department of Education has over the past 70 years become more and more the financier of Higher Education for its citizens.
In the US there are two forms of accreditation. Institutional Accreditation and accreditation by Professional Accreditation Bodies.
Institutional Accreditation is very similar to an ISO quality control system where the processes and physical resources of the institution to measure aggregate standard set by the accreditation agency.
Professional Accreditation Bodies review the programs to see it fulfils the knowledge requirement for the profession the qualification is designed for.
Legally anyone can establish an accreditation agency but to be “recognised” an agency needs to be either a member of the Council for Higher Education Accreditation (CHEA) or recognised directly by the US Department of Education for student funding.
To complicate things some foreign governments, the United Kingdom and United Arab Emirates for example only recognise degrees USA degrees accredited from a regionally accredited schools, not nationally accredited schools (both regional and nationally accredited schools typically are Institutionally Accredited).
I hope this helps your understanding of accreditation a little more.