A parochial institution is one supported by a church or parish--hence the term. It is most often used to describe educational institutions--a parochial school is one in which education is primarly based on religious doctrine. Catholic schools, independent christian church schools, etc. would qualify. If it is found in a news article or story; it would refer to some church based activity. Churches are typically parochial institutions. It also may mean narrow in scope, or limiting ones self to only part of an issue. Those with extreme right wing views might be considered as having a parochial attitude towards the right to keep and bear arms.