What term describes human-made subterranean or hillside passageways used for religious practices?

The term that describes human-made subterranean or hillside passageways specifically used for religious practices is "catacomb." Catacombs are underground burial sites that often served as places for worship, reflection, and remembrance, particularly in early Christian history. They were used not only for interment but also as devotional spaces where individuals could gather in an environment that honored the deceased.

Burial grounds refer generally to any designated area for burying the dead but do not specifically imply the structured, multi-level, and passageway nature of catacombs. Cemeteries are broader locations for burying the dead and can include various types of graves, but they do not specifically denote the underground aspect. Mausoleums are above-ground structures built to house the remains of the deceased, and while they may have religious significance, they do not fit the description of subterranean passageways. Thus, catacombs uniquely embody the characteristics highlighted in the question, making it the correct term.