Short answers, pulled from the story.
The liquid vapor critical point of water occurs at 374 degrees Celsius and 218 atmospheres. At this precise temperature and pressure, the boundary between liquid and vapor vanishes completely.
Charles Cagniard de la Tour first discovered the existence of a critical point in 1822. He showed that carbon dioxide could be liquefied at 31 degrees Celsius at a pressure of 73 atmospheres.
Water becomes compressible and expandable while acting as a poor dielectric near the critical point. It transforms from an excellent solvent for electrolytes to a bad solvent for them.
The van der Waals equation based on mean-field theory predicts wrong scaling laws that fail to match reality near the critical point. This failure means it cannot accurately analyze properties of fluids near the critical point.
Supercritical fluid extraction applies solvency changes to separate compounds efficiently. Supercritical water oxidation uses these unique properties for industrial waste treatment.