a superionic conductor
In an ordinary crystal every ion sits firmly on its assigned lattice site, and to move it must make a rare, hard hop into a vacancy — so ordinary solids are terrible ionic conductors. A superionic conductor is a solid in which one whole family of ions has, in effect, half-melted: while the rest of the crystal stays a rigid, ordinary solid, that one set of ions becomes so mobile it flows almost like a liquid. Picture a stiff scaffold of one kind of atom, with a second kind of atom sloshing freely through the open channels between them like water through a sponge.
The trick is structural: a superionic conductor offers its mobile ions many more available sites than there are ions to fill them, connected by wide, low-barrier channels, so an ion barely has to climb an energy hill to jump to the next empty seat. The textbook example is alpha-silver iodide (alpha-AgI): above 147 degrees C the iodide ions hold a rigid framework while the silver ions become disordered over a large number of nearly-equivalent sites and move with a conductivity around 1 S/cm — comparable to a liquid electrolyte, and a million times higher than an ordinary ionic solid. Other examples move sodium (beta-alumina), oxygen (stabilized zirconia), or lithium (garnet and sulphide electrolytes).
Superionic conductors are the raw material of every solid-electrolyte device: the higher the conductivity, the lower the internal resistance of a fuel cell, sensor, or solid-state battery. Be honest that superionic is a matter of degree, not a sharp switch: researchers loosely call a solid superionic once its ionic conductivity climbs into the range of roughly 10^-4 to 10^-1 S/cm, the useful band for real devices. The frontier prize is a solid that reaches that range at or near room temperature rather than only when red-hot.
In alpha-AgI the silver ions are spread over 42 possible sites for every 2 silver ions per unit cell — a huge surplus of empty seats. With so many nearby vacancies and low barriers between them, the silver sublattice behaves almost like a trapped liquid, giving liquid-like conductivity inside a solid crystal.
A superionic conductor is, loosely, a crystal with a liquid living inside its solid frame.
The 'super' does not mean lossless like a superconductor — it just means unusually fast for a solid. Superionic conduction still dissipates energy as heat and still slows as the material cools.