a course in a university or college consisting largely of independent research terminating in a dissertation or a comprehensive examination, and earning for the student who passes it a degree with distinction.
Examples from the web for honors course
It was an independent research honors course in the philosophy department.
Attendance is a crucial aspect of this honors course.
He went onto a private high school and took the heaviest allowable course load, including every possible honors course.
In terms of the depth of understanding, the honors course has higher expectations for students to be successful.
Unlike dual-credit courses, however, completion of an honors course does not result in college credit.