LORELAI: Oh, look, the Chilton Cheer Society wear matching hats. Eh? Go Harvard.
A school’s Cheer Society exists to financially and practically support its cheer squad. Presumably the parents wear matching hats to identify themselves, and will also cheer for the team from the bleachers.
Lorelai is reminding Rory that everything they’re doing is so Rory can attend Harvard.
The Annotated Gilmore Girls 