The N is probably for "narrative". The QRI is comprised of narrative passages and expository passages. Comprehension levels sometimes vary depending on which text structure is involved.
I haven't seen a recent version of the QRI, but assuming it is still relatively the same in form, it pretty much works like this:
Student is 1:1 with teacher. Student reads passage out loud while the teacher takes a running record. Student then retells the passage (text is removed after initial reading) and then answers a few questions about the passage. Some questions are literal, some are inferential. If a student demonstrates proficiency in both decoding and comprehension then they given the next level up to try. Testing continues until the instructional level is found.
Levels (at least in the version I'm familiar with) extend to 8th grade.
Hope that helps!

Taminy