Lastly, as concerns satisfaction, which as it has, above all the parts of penance, been at all times recommended to the Christian people by our Fathers, so is it the one especially which in our age is, under the highest pretext of piety, impugned by those, who have a form of godliness, but have denied the power thereof: the holy synod declares, that it is absolutely false, and alien from the word of God, that the guilt is never remitted by the Lord, without the whole punishment also being pardoned. For clear and distinct examples are found in the sacred writings, by which, besides by divine tradition, this error is refuted in the plainest manner possible. And, in good truth, the nature of divine justice seems to demand, that in one manner, they, who through ignorance have sinned before Baptism, be received into grace; and in another, those who, after having been freed from the servitude of sin and of the devil, and having received the gift of the Holy Ghost, have not feared, knowingly to defile the temple of God, and to grieve the Holy Spirit. And it becomes the divine clemency, that sins be not in such wise remitted unto us without any satisfaction, as that, occasion being obtained, thinking sins less grievous, we, having done as it were an insult and a despite unto the Holy Ghost, should fall into more grievous sins, treasuring up wrath against the day of wrath. For, without doubt, these satisfactory punishments greatly recall from sin, and restrain as it were with a bridle, and make penitents more cautious and watchful for the future; they also furnish remedies for the remains of sin, and, by opposite acts of the virtues, they remove the vicious habits acquired by evil living. Neither indeed was there any way ever in the Church of God accounted surer to turn away the punishment impending at the hands of the Lord, than that men should, with true sorrow of mind, frequently practise these works of penitence. It adds further to these things, that, whilst we, by making satisfaction, suffer for our sins, we are made conformable to Christ Jesus, who satisfied for our sins, from whom all our sufficiency is; thence, having also a most sure pledge, that if we suffer with him, we shall also be glorified with him. But neither is this satisfaction, which we discharge for our sins, so much our own, as not to be through Jesus Christ. For we who can do nothing of ourselves, as of ourselves, can do all things, He co-operating, who strengthens us. Thus, man has not wherein he should glory, but all our glorying is in Christ: in whom we live; in whom we merit; in whom we satisfy; bringing forth fruits worthy of penance, which from Him derive their virtue; by Him are offered unto the Father; and through Him are accepted by the Father. Therefore the priests of the Lord ought, as far as the Spirit and prudence shall suggest, to enjoin salutary and fitting satisfactions,  according to the quality of the crimes and the ability of the penitents; lest, if by chance they connive at sins, and deal too indulgently with penitents, by enjoining certain very light works for the most grievous crimes, they be made partakers of other men's sins. But let them have before their eyes, that the satisfaction which they impose be not only unto the preservation of a new life, and a medicine for infirmity, but also unto the avenging and punishing of past sins. For likewise, the ancient fathers both believe and teach, that the keys of the priests were given, not to loose only, but also to bind. But not, therefore, did they suppose that the sacrament of Penance is a court of wrath or of punishments; even as no Catholic ever thought, that, by this kind of satisfactions on our part, the virtue of the merit and of the satisfaction of our Lord Jesus is either obscured, or to any extent lessened: which, while the innovators wish to understand, they in such wise teach that a new life is the best penance, as to take away the entire virtue and use of satisfaction.*

The Canons and Decrees of the Council of Trent, Buckley, Theodore Alois,(London: George Routledge and Co., 1851), pp. 95–97

The penitent must "fully satisfy the justice of God." Satisfaction (or penance) is an act of the penitent "by which he makes certain reparation to the justice of God for his sins."

(See the Catechism of St. Pius X; Questions 105, 118, clerus.org)

105 Question. What is satisfaction?

Answer. Satisfaction, which is also called sacramental penance, is one of the acts of the penitent by which he makes a certain reparation to the justice of God for his sins, by performing the works the Confessor imposes on him.

118 Question. Do those who die after having received absolution but before they have fully satisfied the justice of God, go straight to Heaven?

Answer. No, they go to Purgatory there to satisfy the justice of God and be perfectly purified.