1. to enroll in a college or university as a candidate for a degree.
2. to register (a coat of arms), used especially in Scottish heraldry.
From Quick and Dirty Tips.com:
Matriculate is most commonly used as a verb meaning to enroll in or be admitted to a group such as a college, university, or program. When it is used in this way, it is usually followed by a preposition such as at, into, or to.
From Merriam-Webster:
Anybody who has had basic Latin knows that alma mater, a fancy term for the school you attended, comes from a phrase that means "fostering mother." If mater is "mother," then matriculate probably has something to do with a school nurturing you just like good old mom, right? Not exactly. If you go back far enough, matriculate is distantly related to the Latin mater, but its maternal associations were lost long ago. It is more closely related to Late Latin matricula, which means "public roll or register," and it has more to do with being enrolled than being mothered.
Medieval Latin matriculatus, past participle of matriculare, from Late Latin matricula public roll, diminutive of matric-, matrix list