Objection 1. It would seem that there is no necessity for keys in the Church. For there is no need for keys that one may enter a house the door of which is open. But it is written (Apocalypse 4:1): "I looked and behold a door was opened in heaven," which door is Christ, for He said of Himself (John 10:7): "I am the door." Therefore the Church needs no keys for the entrance into heaven.
Objection 2. Further, a key is needed for opening and shutting. But this belongs to Christ alone, "Who openeth and no man shutteth, shutteth and no man openeth" (Apocalypse 3:7). Therefore the Church has no keys in the hands of her ministers.
Objection 3. Further, hell is opened to whomever heaven is closed, and vice versa. Therefore whoever has the keys of heaven, has the keys of hell. But the Church is not said to have the keys of hell. Therefore neither has she the keys of heaven.
On the contrary, It is written (Matthew 16:19): "To thee will I give the keys of the kingdom of heaven."
Further, every dispenser should have the keys of the things that he dispenses. But the ministers of the Church are the dispensers of the divine mysteries, as appears from 1 Corinthians 4:1. Therefore they ought to have the keys.
I answer that, In material things a key is an instrument for opening a door. Now the door of the kingdom is closed to us through sin, both as to the stain and as to the debt of punishment. Wherefore the power of removing this obstacle is called a key. Now this power is in the Divine Trinity by authority; hence some say that God has the key of "authority." But Christ Man had the power to remove the above obstacle, through the merit of His Passion, which also is said to open the door; hence some say that He has the keys of "excellence." And since "the sacraments of which the Church is built, flowed from the side of Christ while He lay asleep on the cross" [Augustine, Enarr. in Ps. 138], the efficacy of the Passion abides in the sacraments of the Church. Wherefore a certain power for the removal of the aforesaid obstacle is bestowed on the ministers of the Church, who are the dispensers of the sacraments, not by their own, but by a Divine power and by the Passion of Christ. This power is called metaphorically the Church's key, and is the key of "ministry."
Reply to Objection 1. The door of heaven, considered in itself, is ever open, but it is said to be closed to someone, on account of some obstacle against entering therein, which is in himself. The obstacle which the entire human nature inherited from the sin of the first man was removed by Christ's Passion; hence, after the Passion, John saw an opened door in heaven. Yet that door still remains closed to this or that man, on account of the original sin which he has contracted, or the actual sin which he has committed: hence we need the sacraments and the keys of the Church.
Reply to Objection 2. This refers to His closing Limbo, so that thenceforth no one should go there, and to His opening of Paradise, the obstacle of nature being removed by His Passion.
Reply to Objection 3. The key whereby hell is opened and closed, is the power of bestowing grace, whereby hell is opened to man, so that he is taken out from sin which is the door of hell, and closed, so that by the help of grace man should no more fall into sin. Now the power of bestowing grace belongs to God alone, wherefore He kept this key to Himself. But the key of the kingdom is also the power to remit the debt of temporal punishment, which debt prevents man from entering the kingdom Consequently the key of the kingdom can be given to man rather than the key of hell, for they are not the same, as is clear from what has been said. For a man may be set free from hell by the remission of the debt of eternal punishment, without being at once admitted to the kingdom, on account of his yet owing a debt of temporal punishment.
It may also be replied, as some state, that the key of heaven is also the key of hell, since if one is opened to a man, the other, for that very reason, is closed to him, but it takes its name from the better of the two.
Source: Summa Theologica (New Advent)