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 or administrative (in many cases colonial) geographical area.
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, i.e. directly subject to the Holy See (notably the Roman Congregation for the Evangelization of Peoples), normally not part of 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.