A matter/antimatter reactor, put simply, is a power source that harnesses the annihilation energy released when matter and antimatter meet. The power output of matter/antimatter reactors using current technology is orders of magnitude greater than more conventional power sources, making them essential for the operation of advanced starship technologies like hyperspace drives and energy shielding.
The biggest technical challenge in engineering a matter/antimatter reactor is finding a safe way to store the antimatter and feed it into the reaction chamber. This goal is most commonly achieved using a storage matrix with heavily shielded outer walls, and magnetic channels within which antimatter ions can flow freely.
The practical challenge in operating a matter/antimatter reactor is acquiring the antimatter in the first place. Manufacturing antimatter is expensive, and handling it is dangerous, so organizations who deal in antimatter are usually highly specialized, and charge a high premium for their product. The actual processes used to generate antimatter are held as trade secrets.