No. 1030 - 1032, pages 268-269 of the Catechism of the Catholic Church, Libreria Editrice Vaticana: Urbi Et Orbi Communications:
[1030]
All who die in God’s grace and friendship, but still imperfectly purified,
are indeed assured of their eternal salvation, but after death they
undergo purification, so as to achieve the holiness necessary to enter
heave.
[1031]
The Church gives the name Purgatory to this final purification of the
elect, which is entirely different from the punishment of the damned
(604).
The Church formulated her doctrine of faith on Purgatory especially at
the Councils of Florence and Trent. The tradition of the Church, by
reference to certain texts of Scripture, speaks of a cleansing fire
(605).
As for certain lesser faults, we must believe that, before the Final
Judgment, there is a purifying fire. He who is truth says that whoever
utters blasphemy against the Holy Spirit will be pardoned neither in
this age nor in the age to come. From this sentence we understand
that certain ofenses can be forgiven in this age, but certain others in
the age to come (606).
[1032]
This teaching is also based on the practice of prayer for the dead,
already mentioned in Sacred Scripture: "Therefore {Judas
Maccabeus} made atonement for the dead, that they might be
delivered from their sin." (607).
From the beginning the Church has honored the emory of the dead
and offered prayers in suffrage for them, above all the Eucharistis
sacrifice, so that, thus purified, they may attain the beatific vision of
God (608).
The Church also commends almsgiving, indulgences, and works of
penance undertaken on behalf of the dead:
Let us help and commemorate them. If Job’s sons were purified by
their father’s sacrifice, why would we doubt that our offerings for the
dead bring them some consolation? Let us hot hesitate to help those
who have died and to offer our prayers for them (609).
1381:
Q: What is Purgatory?
A: Purgatory is the state in which those suffer for a time who die
guilty of venial sins, or without having satisfied for the punishment due
to their sins.
1382:
Q: Why is this state called Purgatory?
A: This state is called Purgatory because in it the souls are purged or
purified from all their stains; and it is not, therefore, a permanent or
lasting state for the soul.
1383:
Q: Are the souls in Purgatory sure of their salvation?
A: The souls in Purgatory are sure of their salvation, and they will
enter heaven as soon as they are completely purified and made
worthy to enjoy that presence of God which is called the Beatific
Vision.
1384:
Q: Do we know what souls are in Purgatory, and how long they have
to remain there?
A: We do not know what souls are in Purgatory nor how long they
have to remain there; hence we continue to pray for all persons who
have died apparently in the true faith and free from mortal sin. They
are called the faithful departed.
1385:
Q: Can the faithful on earth help the souls in Purgatory?
A: The faithful on earth can help the souls in Purgatory by their
prayers, fasts, alms-deeds; by indulgences, and by having Masses
said for them.