The Heisenberg compensator was a component of the transporter system. The compensator worked around the problems caused by the Heisenberg Uncertainty Principle, allowing the transporter sensors to compensate for their inability to determine both the position and momentum of the target particles to the same degree of accuracy. This ensured the matter stream remained coherent during transport, and no data was lost.
A scan of the Heisenberg compensators, to ensure they were performing within the specified parameters, could be performed by raising the transporter pad. (TNG: "Realm of Fear")
While trying to devise a way to transport holographic matter off the holodeck without it disintegrating instantly, the idea was put forth that decoupling the Heisenberg compensators might let the matter reform normally, although the suggestion was used as a stalling tactic against ProfessorJames Moriarty, and the idea had never actually been tried before. (TNG: "Ship in a Bottle")
The Heisenberg compensator was invented to circumvent the authors' understanding of the Heisenberg uncertainty principle, which they believed to state that one cannot know both the position of a subatomic particle and its momentum to arbitrary precision. (Star Trek Encyclopedia, 3rd ed., p. 187)
When asked by Time magazine in 1994, "How do the Heisenberg compensators work?" Michael Okuda replied, "They work just fine, thank you."