Until after the destruction of Jerusalem by Titus (A.D. 70) the Christians were regarded as a sect of the Jews; hence those Jews who were converted by the Apostles at Rome were buried in the catacombs of their fellow-countrymen. The question arises as to where those converted from heathenism by the Apostles found their last resting-place. It is a fact to which Tacitus, Suetonius, Dio Cassius, and other pagan historians bear witness, that as early as the days of the Apostles members of the higher and of even of the highest ranks of the nobility had become Christians. These converts of rank from heathenism had their own tombs, and permitted their brethren in the Faith to construct, in connection with these family tombs, places of burial modelled on the Jewish catacombs. This is the origin of the Christian catacombs.
Excerpted from The Catholic Encyclopedia.