Honorific term for someone's judgment or discernment, often used in the set phrase お眼鏡にかなう (to meet with someone's approval).
See also: 眼鏡にかなう
I'll do my best to come up with a plan that meets the department head's approval.
She won the president's favor and was selected as the leader of the new project.
Derived from 眼鏡 (めがね, 'glasses') with the honorific prefix お, metaphorically extending the idea of 'looking through glasses' to mean 'judgment' or 'discernment'.