The story
Referring to the bell curve of a normal distribution.
Etymology from Wiktionary, CC BY-SA 4.0.
grade on a curve
Today it means: To use a grading system based on the scale of performance of a group to normalize a right-skewed grade distribution (with more lower scores) into a bell curve, so that more can receive higher grades, regardless of their actual knowledge of the subject; to curve a grade. Full definition →