A metaphysical engine was a device that allowed travel into the minds or thoughts of individuals, or groups of people, including their beliefs and imaginations.
According to the First Doctor, the TARDIS was a metaphysical engine. As it could travel through all dimensions related to space and time, it was also capable of entering into a person's mind, their imagination. Once, the TARDIS entered the mind of George Smythe, who was trapped in a time loop. (PROSE: Every Day)
The Governors had one such metaphysical engine, also called a reliquary. The device they acquired was very old technology, and quite unstable. It could only travel into places believed in by large enough groups of people, such as their afterlife myths. (TV: The Metaphysical Engine, or What Quill Did)