What is the meaning of "superionic"? I see the term "superionic" applied to high pressure water in articles like Giant planets may host superionic water, but I don't understand what the term really means.  

How is "superionic" distinguished from simply "ionic"?  

Why does the article refer to hydrogen "atoms", which would imply that they are neutral, as opposed to protons or hydronium or some other actual ion?
Superionic water is water under extreme heat and temperature with the properties of both solids and liquids. 
It is where the water only exists as a mixture of $\ce{H+}$ and $\ce{OH-}$ ions. At high pressures, the oxygen crystallises, leaving the hydrogen ions free - thus making superionic water highly conductive.
It's crystal structure is a face-centred cubic lattice, and it is thought that Uranus and Neptune hold a layer of superionic water.