Subspace is an alternate dimension referred to in many science fiction settings. While the details of subspace vary, a common characteristic is that subspace phenomena and technologies can defy the known laws of physics by exceeding the speed of light.
Star Trek Subspace
In Star Trek, subspace lies behind many futuristic technologies. "Subspace fields" allow ships to travel at faster-than-light speeds, for instance. Messages transmitted through subspace also travel faster-than-light. Mass-lightening is another subspace technology that somehow reduces the inertial mass of a starship, allowing it to accelerate quickly with a small amount of thrust for its true mass.
Normally, subspace only influences objects in normal space within the confines of a technologically created subspace field. The separation between normal space and subspace can thin, however, where intense subspace fields are used regularly. For example, constant warp-speed starship traffic through the Hekaras Corridor thinned the barrier between normal space and subspace, and the subsequent self-destruction of a starship's warp drive in the corridor created a rift between the dimensions. (TNG, "Force of Nature")
According to Star Trek engineers, subspace has multiple layers or "domains". At least one subspace domain is inhabited. (TNG, "Schisms")