Q: Why do we call it a parish?
A: Parish is the Engilsh equivalent of Paroecia (Latin). It is defined as "a certain community of the Christian faihtful stably constituted in a particular church, whose pastoral care is entrusted to a pastor (parochus/parish priest) as its proper pastor (pastor/priest) under the authority of the diocesan bishop." (Canon 515 from Code of Canon Law).
A simple note of explanation with the different terms of parochus and pastor. A pastor is any priest validly ordained by a valid bishop, what we would simply call a priest. A parochus is a pastor that has been assigned to a certain parish, or group of stable faithful in a certain territory. In everyday speech, they are the same...in the law there is a key difference. Canon 519 explains this distinction in the words of law:
"The pastor (parochus) is the proper pastor (pastor) of the parish entrusted to him, exercising the pastoral care of the community committed to him under the authority of the diocesan bishop in whose ministry of Christ he has been called to share, so that for that same community he carries out the functions of teaching, sanctifying, and governing, also with the cooperation of other presbyters ordeacons and with the assistance of lay members of the Christian faithful, according to the norm of law."