A Pontifical Delegate is a cleric who is delegated by the Pope of Rome.
Specifically, this title is used for the following ecclesiastical offices in the gift of the Pope (who is Pontifex Maximus, hence the adjective) :
a prelate (usually Archbishop of Cardinal) appointed to represent the Holy See in the administration of certain papal minor basilicas, notably:
Pontifical Delegation for the Basilica of St. Nicholas of Bari
Pontifical Delegation for the Shrine of the Holy House of Loreto
Pontifical Delegation for the Basilica of St. Anthony of Padua
Pontifical Delegation for the Shrine of Our Lady of the Rosary of Pompeii
a papal legate, papal diplomat, such as a Nuncio
an extraordinary papal representative to a religious congregation, e.g. the thirty third General Congregation of the Jesuits
a papal representative, appointed to exercise certain rights reserved, thus limiting the authority of a Major archbishop, as in the case of the Syro-Malabar Catholic Church