Accreditation, both for conventional and online degrees, is uniquely American, although there are standards by which American schools evaluate non-US programs for equivalency (specialists normally refer to them as Generally Accepted Accreditation Principles, or GAAP).
The most widely recognized offline and online degree accreditors are the six regional accrediting bodies. They accredit nearly all of the "bricks-and-mortar" schools in the U.S., along with a small number of distance education-only programs. The Distance Education and Training Council (DETC) is also a recognized accreditor focused on schools with distance learning and online degree programs. Whether due to its history as a vocational accreditor or for other reasons, DETC-accredited degrees are not as widely accepted as regionally accredited ones; a recent study showed that less than 50% of regionally accredited schools would accept transfer credits or recognize degrees from DETC-accredited schools, and at least some employers require regionally accredited degrees. So, while there are many good DETC-accredited schools, you will have the most options and flexibility in your future if you choose a regionally accredited school.
Online degree accreditation is a long, complex, and expensive process for schools, and while imperfect (the education received at Harvard and at a typical rural community college is probably not equivalent) accreditation does provide a minimum standard for quality education.
We suggest that students investigate schools carefully and consider accreditation as a critical factor. In general, regional accreditation will mean greater acceptance of the online degree. With a very few exceptions, unaccredited online degree schools are a risky choice.