During the Entrance Procession, when the priest and his ministers reach the entrance to the sanctuary, they make a sign of reverence, a bow of the body to the altar. (If the tabernacle with the Blessed Sacrament is in the sanctuary, then instead of bowing to the altar, they should genuflect to the Blessed Sacrament.) Then the priest ascends to the altar and kisses it before going to his chair; the deacon kisses the altar as well. On particularly solemn occasions, the priest may even bless the altar with incense. Why is all this attention paid to the altar? Because the altar is a sign of Christ; according to one of the Prefaces for the Eucharistic Prayer during the Easter season, Christ is the “sacerdos, altare et agnus” (“priest, altar, and lamb”) of His sacrifice.
It is easy to recognize Christ as the priest and the lamb (that is, the victim); why He is the altar deserves some explanation to our modern minds. St. Ambrose, bishop of Milan in the fourth century and spiritual father of St. Augustine, took the image of Christ-as-altar for granted in his treatise De Sacramentis, where he writes (without much explanation) that “the altar is a type [i.e. sign] of the body [of Christ]” (Book IV, 7) and then again almost as an aside, “for what is the altar but the type of the body of Christ?” (Book V, 7)
Consider first the composition of the altar. Traditionally, the altar is made of stone and is immovable – although some countries, such as the United States, may use wood for the altar, provided it is “worthy, solid, and well-crafted.” (GIRM 301) Why stone for the altar? St. Paul speaks of Christ as “the supernatural Rock” that accompanied the Israelites in the desert during their exodus from Egypt, the Rock from which flowed water for their sustenance. (1 Cor. 10:4; cf. Ex. 17:6) Sts. Paul and Peter identified Christ as the “cornerstone” (Eph. 2:20; 1 Pet. 2:6), and Jesus used this language referring to Himself. (cf. Luke 20:17-18) The concept is found in Psalm 118:22-26, the very same psalm that the inhabitants of Jerusalem sang as Jesus entered their city.
Not only is Christ “that living stone” (1 Pet. 2:4), but we too are called to be “living stones.” (1 Pet. 2:5) This means the altar is also a sign of the Church, made up of diverse people, living stones, gathered and built into one, in peace and unity. St. Paul described the Church as being made up of those Jews and Gentiles who accepted Christ, and that Christ “is our peace, who has made us both [Jew and Gentile] one.” (Eph. 2:14) Jesus “kissed [this altar, the Church] in the middle” with the “holy kiss of peace and unity” (Douay Catechism 125), so the priest imitates Christ in kissing the altar and in doing so, shows “a sign of his affection and close adherence to Christ.” (The Glories of the Catholic Church, p. 222)
Now consider what takes place on the altar. An altar is a place of sacrifice, a place of offering something to God, a place of encountering God. Jesus offered Himself on earth on the “altar of the cross,” and that offering is now made present on the Church’s altar. The altar is related to our Lord’s Passion and represents the cross, so the priest bowing before the altar “signifies the prostrating of Christ in the garden, when he began his passion.” (Douay Catechism 125; cf. Matt. 26:39) Jesus went so far as to identify the Temple (and its altar) with Himself:
Jesus [said], “Destroy this temple, and in three days I will raise it up.” The Jews then said, “It has taken forty-six years to build this temple, and will you raise it up in three days?” But he spoke of the temple of his body. (John 2:19-21)
“For which is greater, the gold or the temple that has made the gold sacred? … For which is greater, the gift or the altar that makes the gift sacred?” (Matt. 23:17-19)
Jesus is the “gift” being offered on the altar, but He makes it clear that the altar makes the gift sacred; you certainly would not offer a sacrifice on an altar less dignified than the sacrifice itself. That makes Jesus (Who sanctifies) both the gift and the altar.
Rev. Maurice de la Taille, SJ, meditating upon Christ as altar in his 1915 book The Mystery of Faith, illuminates further:
Those who desired to offer sacrifices to God, had to do so necessarily through an altar. But Christ, the Victim of salvation, approached to God through Himself. Hence He was also the altar of His own sacrifice. For us too in like manner, He is the altar of every one of our sacrifices, for we can bring no offering to God except through Christ. (Chapter 5, Section 2)
Not only did Christ approach the Father through Himself as an altar, but now Christ is our altar through Whom we approach the Father. St. Paul exhorted the Romans, “present your bodies as a living sacrifice, holy and acceptable to God, which is your spiritual worship.” (Rom. 12:1) This thought was taken up by St. Peter who completed it when he wrote that we are “to offer spiritual sacrifices acceptable to God through Jesus Christ.” (1 Pet. 2:5) It is no accident that we offer our prayers to God “through Christ our Lord.”
In the Extraordinary Form of the Mass, two prayers accompany the approaching and kissing of the altar. As he ascends the steps to the altar, the priest prays that the Lord remove our iniquity so that we might enter the Sancta Sanctorum (“Holy of Holies”) worthily, with pure minds. This prayer is not present in the Ordinary Form, but the priest should still be aware of its sentiment as he approaches the altar of sacrifice. In the prayer that accompanies the kissing of the altar, the priest asks God pardon for his sins, by the merits of His “saints whose relics are here” and of all the saints. While this prayer is not found in the Ordinary Form, the Church has retained the ancient tradition of placing relics of saints within the altar stone. (GIRM 302) This practice calls to mind the early history of the Church, when persecuted Christians used martyrs’ tombs for altars. (Baltimore Catechism III 937) By kissing the altar above the place where the relics are reserved, the priest silently declares his union with and affection for the saints who have gone before him. This kiss is a “holy kiss” (Rom. 16:16), a “kiss of love” (1 Pet. 5:14), for Christ and for His Church and her members. It is a kiss by which we begin to learn that the liturgy is “the purest and most sublime school of love.” (The Splendour of the Liturgy, p. 38)
 According to Rev. Jean Danielou, S.J., this expression can be traced to St. Cyril of Alexandria and Origen. (cf. The Bible and the Liturgy, p. 130)
 In the Extraordinary Form, the Penitential Act happens before the priest goes to the altar, while in the Ordinary Form, the Penitential Act happens after he has gone to the altar. This may explain this prayer’s omission from the Ordinary Form.