Superconductivity is a phenomenon that occurs in many metals, alloys, and other substances, at low temperatures, involving zero electrical resistance and perfect diamagnetism. In a superconducting material an electric current will persist indefinitely without any driving voltage and applied magnetic fields are exactly cancelled out by the magnetization they produce.
In type I superconductors, both these properties disappear abruptly when the temperature or applied magnetic field exceed critical values (typically 5K and 104 A/m), but in type II semiconductors the diamagnetism decay is spread over a range of field values. Large electromagnets sometimes use superconducting coils which will carry large currents without overheating, and the exclusion of fields by superconducting materials can be exploited to screen or direct magnetic fields.
Superconductivity was discovered by Hans Kamerlingh-Onnes in 1911, and is due to an indirect interaction of pairs of electrons via local elastic deformation of the metal crystal. The theory explaining it is called the BCS theory.