Something that's scholastic has to do with schools or learning. If you brag about your town's scholastic excellence, you mean that you've got great schools.
When your school principal talks about scholastic achievement, she's discussing the grades and test scores of her students, and if you referred to your own scholastic challenges, you probably mean the subjects you find the most difficult in school. One well-known US college entrance exam is the SAT, which is an acronym for "Scholastic Aptitude Test." The word is from the Latin scholasticus, "of a school," with the Greek root skholastikos, "devoting one's leisure to learning."