Longman Dictionary of Contemporary English
Wiktionary
n. A school associated with the parish of a church.
WordNet
n. a private religious school run by a church or parish [syn: church school]
Wikipedia
A parochial school is a private primary or secondary school affiliated with a religious organization, and whose curriculum includes general religious education in addition to secular subjects, such as science, mathematics and language arts. The word "parochial" comes from the same root as "parish", and parochial schools were originally the educational wing of the local parish church. Christian parochial schools are often called "church schools". In Ontario, parochial schools are called "separate schools."
In addition to schools run by Christian organizations, there are also Jewish (Hebrew), Muslim and other schools. These, however, are not usually called "parochial" because of the term's historical association with Christian parishes.