An apostolic prefect or prefect apostolic is a priest who heads what is known as an apostolic prefecture, a 'pre-diocesan' missionary jurisdiction where the Catholic Church is not yet sufficiently developed to have it made a diocese. Although it usually has an (embryonal) see, it is often not called after such city but rather after a natural feature, or administrative geographical area, which may be a name in use by the local inhabitants, or one assigned by a colonial authority, depending on the circumstances under which the prefecture was established.
If a prefecture grows and flourishes, it may be elevated to an apostolic vicariate, headed by a titular bishop, in the hope that with time the region will generate enough Catholics and stability for its Catholic institutions, to warrant being established as a diocese. Both these stages remain missionary, hence exempt, that is, directly subject to the Holy See, specifically the Dicastery for Evangelization, rather than, as a diocese normally would, belong to an ecclesiastical province.
The full sequence of development is: independent mission, apostolic prefecture, apostolic vicariate, apostolic diocese; however steps may be skipped at the papal discretion, so the next steps may be bishopric or even archbishopric.
The apostolic prefecture and the apostolic vicariate are to be distinguished from the territorial abbacy (formerly called an "abbey nullius").