A priory is a monastery of men or women under religious vows that is headed by a prior or prioress.
Priories may be monastic houses of monks or nuns (such as the Benedictines, the Cistercians, or the Charterhouses).
Houses of canons & canonesses regular also use this term, the alternative being "canonry".
The bishop, in effect, took the place of the abbot, and the monastery itself was headed by a prior.
[1] The Benedictines and their offshoots (Cistercians and Trappists among them), the Premonstratensians, and the military orders distinguish between conventual and simple or obedientiary priories.