The bridge of the Dauntless in mid-transformation.
Particle synthesis is a technology that creates illusory objects, much like holographic technology, but more advanced.
In 2374, Arturis employed particle synthesis aboard his ship, the Dauntless, to simulate a Starfleet appearance. On the bridge of his craft, Arturis could activate a computer command and reconfigure the room to any design he wished. (VOY: "Hope and Fear")
In 2375, Species 8472 used particle synthesis along with holographic technology to create a simulation of Starfleet Headquarters in their terraspheres. (VOY: "In the Flesh")
Apocrypha
According to the Pocket Books novel Greater than the Sum, particle synthesis is related to the Quantum Slipstream technology. In the novel, it is explained that the particle synthesis works by exploiting, and altering, virtual particles on a quantum level.