The word "honors" is used a lot in school documents, and I know it has slightly different meanings depending on wheres and whats. This is the context for this question:
I'm reading an American document describing a university's grading system. There's "High Honors Quality", "Basic Honors Quality" and "Below Honors Quality". I don't get what "honors" is supposed to represent. For example, "Below Honors Quality" is better than "Above Satisfactory Quality", what sounds... Oddly counter-intuitive for someone unfamiliar with English-speaking countries' school systems.
That is specific to various local school systems.
When I was in school in Ontario, Canada, being on the "honour roll" meant having an average of over 80%. We didn't use those other terms.
It's an arbitrary benchmark for that specific school for recognizing academically-successful students. Different schools will have different requirements for "honors", but they all more or less equate to the school formally acknowledging that a student did well at that school.
There is no specific standard for it. But typically a student can graduate “with honors” if they have a high enough grade average compared to the rest of the school. The school determines that the top percentage of students will get a special recognition for it, but beyond that it does not mean much.
We use it very differently in the UK. Most undergraduate degrees are "with Honours", but if your grades are too low you may graduate with an "ordinary degree". That's a final mark between 30 to 39.9%.
I think originally the idea was that an ordinary degree was a standard and honours was for higher achievement, but in practice these days First Class Honours are considered a high achievement, second class (upper and lower) are considered quite standard, and third class honours or an ordinary degree are considered tantamount to failure.
Honors means that, within the school giving the honors, you'd did better than average, well enough to meet the benchmark that specific school set for honors.
The definition for this school will be in its student handbook.