Catholics kiss relics because of what we believe about the human body. Relics are either parts of saints bodies or material objects (like clothing) that have been touched by a saint.
Kissing these relics is a way of honoring the saint and how God has worked through their lives. While honoring a piece of bone might seem strange, you have to remember that every person is both body and soul. When someone dies their soul and body separate, however this separation is only temporary. When Christ comes at the end of time, all of the saints in heaven will be reunited with their bodies.
We venerate the bodies of saints because even though the saint is dead they are still an important part of that man or woman. They were once temples of the Holy Spirit (1 Corinthians 6:15) and one day they will be eternally glorified!
In several places in the Bible we see how important the body is, even after death. For example in the book of Kings a dead man falls into the grave of Elisha the prophet and then is healed! 'As soon as the man touched the bones of Elisha, he revived and stood on his feet' (2 Kings 13:21).
Just as God draws us closer to him through the lives of holy people, it makes sense that they would continue to draw us to God even by just their physical remains after death. What about pieces of clothing that the saint touched? Why should we honor these? In the book of Acts we read how God did extraordinary miracles through St. Paul. It says that even handkerchiefs or aprons that touched his body caused miracles (Acts 19: 11-12).
God likes to work though physical things, because we are physical creatures – body and soul!