catacombs were, to put it simply, stone-walled underground cemeteries, usually for one or more wealthy Roman families. In that sense, St. Priscilla's catacombs on the Via Salaria, are really no different than many others in the city of Rome. However, painted on the walls of these catacombs are numerous frescos dated to the 2nd and 3rd centuries AD.
One of the frescoes illustrates a woman presiding over the Eucharist (not a thing that the Christian church of a few centuries later would consider even possible), while another has been interpreted by some scholars as a representation of St. Peter.
For more on St. Priscilla and other catacombs, see the article by Martha Bakerjian, About's Guide to Italy for Travelers, called Catacombs in Italy