In Ancient Rome, it was against the law to bury the dead inside the city, so that the dead bodies would not pollute their water source. However, the Romans cremated their dead relatives and kept the ashes of the dead in urns. Christians could not do this because they believe that the body is an important part of who we are. When Christ resurrected, he was resurrected body and soul. So, the Christians took the bodies of their deceased relatives outside the city and dug out catacombs in which to bury them.
Ancient Christians dug the catacombs out of what is called tufa stone, which is compressed volcanic ash. It is brittle and soft, easy to dig into. They dug out narrow corridors with shelves on either side (photo above), in which they laid their dead. Whenever they needed more space, the Christians of ancient Rome would dig further out or deeper down. Eventually, catacombs became labyrinthine microcosms beneath the Italian soil just outside of Rome.
Resource: our Virtual Pilgrimage on Early Christian Worship and Symbolism part 1 (watch on YouTube here)