Catacombs were underground chambers and passageways, often beneath a religious establishment and usually having a religious function, such as the storage of relics or sainted bodies.
In 2151 Trip Tucker used a transmitter in the catacombs hidden beneath the monastery at P'Jem to contact Enterprise NX-01 after the landing party's communicators had been destroyed by Thy'lek Shran. Later, Captain Jonathan Archer defused the stand-off with the Andorians by discovering within a nearby reliquary the entrance to a massive subsurface sensor array. (ENT: "The Andorian Incident")
The blueprints for this set were later sold off on the It's A Wrap! sale and auction on eBay along with a script of the episode. [1](X)
Archer explored another set of Vulcan catacombs in 2154. He identified the 1800-yr-old mummified remains of T'Klaas, a student of Surak, in a passage beneath the T'Karath Sanctuary. (ENT: "Awakening")
The Children of the Son cave on planet 892-IV to which Kirk, Spock and McCoy were taken in TOS: "Bread and Circuses", while not technically underground, would seem to be an echo of the catacombs that sheltered Earth's early Christian outlaws.