Our Lord requires us to believe in it as a matter of Faith, as purgatory is a dogma of the Church.
During the Sacrament of Confession the priest gives a penance. This is the sign of purgatory. The penance given is not the whole penance due, it is merely to help one begin.
The souls of the just which, in the moment of death, are burdened with venial sins or temporal punishment due to sins, enter Purgatory. (De Fide.)
- Fundamentals of Catholic Dogma
"The souls of those who depart this life with true repentance and in the love of God, before they have rendered satisfaction for their trespasses and negligences by the worthy fruits of penance, are purified who depart this life with true repentance of purification."
“Among them is also the fire of purgatory, in which the souls of just men are cleansed by a temporary punishment, in order to be admitted into their eternal country, into which nothing defiled entereth. The truth of this doctrine, founded, as holy Councils declare,’ on Scripture, and confirmed by Apostolic tradition, demands exposition from the pastor, all the more diligent and frequent, because we live in times when men endure not sound doctrine.”
- Catechism of Council of Trent
“The faithful must be fully aware that sin and its eternal punishment are remitted by the Sacrament of Penance if one makes proper use of it; however the entire temporal punishment is very seldom taken away. This must be removed either by satisfactory works in this life or by the fire of Purgatory after death. The holy Council of Trent in session 6, chap. 4, and canon 30 of the same session teaches this under the heading* de Justification*e.”
Pope Benedict XIV, Apostolic Constitution, On Preparation for the Holy Year