Objection 1. It would seem that the priest cannot bind by virtue of the power of the keys. For the sacramental power is ordained as a remedy against sin. Now binding is not a remedy for sin, but seemingly is rather conducive to an aggravation of the disease. Therefore, by the power of the keys, which is a sacramental power, the priest cannot bind.
Objection 2. Further, just as to loose or to open is to remove an obstacle, so to bind is to place an obstacle. Now an obstacle to heaven is sin, which cannot be placed on us by an extrinsic cause, since no sin is committed except by the will. Therefore the priest cannot bind.
Objection 3. Further, the keys derive their efficacy from Christ's Passion. But binding is not an effect of the Passion. Therefore the priest cannot bind by the power of the keys.
On the contrary, It is written (Matthew 16:19): "Whatsoever thou shalt bind on earth, shall be bound also in heaven."
Further, rational powers are directed to opposites. But the power of the keys is a rational power, since it has discretion connected with it. Therefore it is directed to opposites. Therefore if it can loose, it can bind.
I answer that, The operation of the priest in using the keys, is conformed to God's operation, Whose minister he is. Now God's operation extends both to guilt and to punishment; to the guilt indeed, so as to loose it directly. but to bind it indirectly, in so far as He is said to harden, when He withholds His grace; whereas His operation extends to punishment directly, in both respects, because He both spares and inflicts it. In like manner, therefore, although the priest, in absolving, exercises an operation ordained to the remission of guilt, in the way mentioned above (Article 1), nevertheless, in binding, he exercises no operation on the guilt; (unless he be said to bind by not absolving the penitent and by declaring him to be bound), but he has the power both of binding and of loosing with regard to the punishment. For he looses from the punishment which he remits, while he binds as to the punishment which remains. This he does in two ways--first as regards the quantity of the punishment considered in general, and thus he does not bind save by not loosing, and declaring the penitent to be bound, secondly, as regards this or that particular punishment, and thus he binds to punishment by imposing it.
Reply to Objection 1. The remainder of the punishment to which the priest binds the penitent, is the medicine which cleanses the latter from the blemish of sin.
Reply to Objection 2. Not only sin, but also punishment is an obstacle to heaven: and how the latter is enjoined by the priest, has been said in the article.
Reply to Objection 3. Even the Passion of Christ binds us to some punishment whereby we are conformed to Him.
Source: Summa Theologica (New Advent)