I once told a new convert to Catholicism that he needs to understand the Church very well to enjoy our way of worship. In many cases, our Catholic faith is enshrined; our liturgy is full of signs and symbolism, and that makes some none Catholics criticise Catholicism out of ignorant. One of the signs many people including some few Catholics do not understand is the kissing of the altar by the priest at the beginning and at the end of Mass.
At the beginning of the Mass the priest kisses the altar, so many Catholics have become so familiar with this gesture that they no longer attach any meaning to it. But it is a sign, a gesture that expresses something very significant about our Catholic Tradition.
The altar to begin with is a table of sacrifice where the body and blood of Jesus Christ is offered to the Father. At Mass, Jesus is the priest, the victim of the sacrifice and the altar. How he is the priest and the victim of the sacrifice I presume you know (in case you don’t, he acts in the priest and he is the Lamb of the sacrifice), but how Jesus is the altar may make you wonder.
Traditionally the altar is made of stone which symbolically represents Christ the corner stone, we express our faith in Christ who was rejected but became the key stone. The altar is also traditionally not moveable which symbolically expresses our faith in Christ the unmoved mover of all things. So, the priest kisses the altar as a sign of respect and love for Christ as well as greetings. He also kisses the altar to venerate the relic of the saints buried under the altar.
The Church has the tradition of burying the relic of saints under the altar , the history behind this tradition is interesting. During the first centuries of church history, Masses were often celebrated in the underground catacombs on stone slabs covering the tomb of a martyr. This was done in order to reverence the martyr and their heroic and ultimate sacrifice for the Lord. This also was done out of necessity: Being a Christian was illegal throughout the Roman Empire (thus the existence of martyrs) and the Mass had to be celebrated in secret. But as Christianity became legal and Churches were built, the relic of saints were put under the altar rather than going to their tombs.
Kissing of the altar by the priest before the Mass begins is therefore a sign of greeting, respect and love for Christ who is the priest, the altar and the Lamb of the sacrifice. And it is also to venerate the relic of the saints.