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My UG has AACSB accreditation, which is the "Association to Advance Collegiate Schools of Business".

Is this significant in terms of showing the quality of the UG school? I'm simply wondering if this might help demonstrate rigor to Law Schools, given my University is probably not well known to them.

http://en.wikipedia.org/wiki/AACSB
http://www.aacsb.edu/General/InstLists.asp?lid=3

How does this apply to you if you are not studying at their business school?

yes, it does. In fact, I'd write a separate addendum about your schools AACSB accreditation.

How does this apply to you if you are not studying at their business school?

My UG is in Business...