There is a document from the late 11th century that refers to a scola grammatice [grammatic/grammar school]. We see that and similar phrases becoming more common in the 1200s. In 1387 we get the first reference in English to a "gramer scole" by John of Trevisa (briefly mentioned here), who is translating Ralph Higden's Polychronicon* and uses the phrase to refer to a school in Alexandria.
But what did they mean by "grammar" school? Was it all just about teaching grammar. Well, in a word, probably "yes." The term grew to distinguish those schools from the more involved curriculum of the schools that were tackling the seven Liberal Arts—Grammar, Rhetoric and Logic made up the foundational "Trivium" while the higher learning of the Quadrivium meant studying Arithmetic, Geometry, Music, Astronomy. (The first three were all about mastering language, the four were all about mastering mathematics.)
What was covered in "grammar" schools? Well, it was synonymous with what a later age called the study of "letters," and comprised learning from great writings. Grammar school was all about reading great literature from the past and committing the lessons found therein to heart. One learned how the great writers—who could on rare occasions be pagan writers, but were mostly the Church Fathers, as well as the Latin Bible—constructed their brilliant sentences and built their arguments.
Of course, these great minds of the past did not write in English, and so the study of "grammar" could not truly be undertaken until one learned Latin. For young boys beginning instruction—usually at a nearby church under the tutelage of a priest—the first stage was learning Latin.
Latin grammar had been dissected and discussed at great length by scholars in the past, particularly by two Latin writers named Priscian and Donat. But let's save them for tomorrow.
*This work was an attempt to write a universal history, hence the name meaning "many times."
