Territorial prelate

A territorial prelate is, in Catholic usage, a prelate whose geographic jurisdiction, called territorial prelature, generally does not belong to any diocese and is considered a particular church.
The term is also used in a generic sense, and may then equally refer to an apostolic prefecture, an apostolic vicariate, a permanent apostolic administration, or a territorial abbacy.

Status

A territorial prelate exercises quasi-episcopal jurisdiction in a territory separate from the territory of a diocese. In many cases the prelature is exempt from diocesan oversight and instead subject to the jurisdiction of the Holy See.
As a rule, territorial prelates are consecrated as bishops, though not bishops of their diocese, as expressed by the title Bishop-prelate. Most were/are missionaries, outside Europe or in countries with a Protestant majority.

Prelate nullius

The territorial prelate is sometimes called a prelate nullius, from the Latin nullius diœceseos, prelate "of no diocese," meaning the territory falls directly under the 'exempt' jurisdiction of the Holy See or Pope and is not a diocese under a residing bishop.
The rights of prelates nullius are quasi-episcopal, and these dignitaries are supposed to have any power that a bishop has, unless it is expressly denied to them by canon law. If they have not received episcopal consecration, such prelates may not confer holy orders. If not consecrated episcopally, they have not the power to exercise those functions of consecrating oils, etc., which are referred to the episcopal order only analogously.
Prelates nullius may take cognizance of matrimonial causes within the same limits as a bishop. They may dispense from the proclamation of matrimonial banns, grant faculties for hearing confessions and preaching, reserve certain cases to themselves, publish indulgences and jubilees, exercise full jurisdiction over the enclosure of nuns, and invite any bishop to confirm in their quasi-diocese. They may, even if priests only, confirm themselves by papal privilege as expressed in canon 883 No. 1 CIC whenever they find it appropriate; however, even as local ordinaries they are in that case only extraordinary ministers of confirmation and should thus prefer to invite bishops if possible.
These prelates may not, however, without special permission of the Holy See, convoke a synod or institute synodal examiners. Neither may they confer parochial benefices. They are not allowed to grant indulgences, or absolve from the reserved cases and secret irregularities whose absolution is restricted to the pope ordinarily, but allowed to bishops by the Council of Trent, nor promote secular clerics to orders, nor grant dimissory letters for ordination, nor exercise jurisdiction over regulars as apostolic delegates.
Prelates nullius are, however, bound to residence, to preach the Word of God, to offer Mass for their people, to make the visit ad limina to the Roman Curia, and in concurrence with the neighbouring bishop to perform a visitation of their quasi-diocese.