Grammar in the broad sense is our collective memory, our store of knowledge, our cultural capital. It is the Who, What, When and Where.
She is a teacher, a parent, a goddess. She is Juno. She teaches the rules, history and culture to a new generation.
The 7 Squares on her dress represent the 7 Liberal Arts:
Grammar, Logic, Rhetoric (The Trivium)
Arithmatic, Geometry, Music, Astronomy (The Quadrivium)
Liberal arts: the arts to be learnt by a free man, the arts to set a man free.