A crematorium is the building where dead bodies are burned as part of a funeral. Inside there is a special very hot furnace, and often a room where relatives can sit. The word is formal. American English also uses crematory for the same kind of place. Though actually, the hall where people say goodbye and the crematorium where the burning happens are not always the same building, even when people use one name for the whole visit. A cemetery is different again: that is where bodies or ashes are laid to rest.