Short answers, pulled from the story.
A critical point is the endpoint of a phase equilibrium curve, where the boundary between two phases of matter vanishes. At the liquid-vapor critical point, the distinction between liquid and vapor disappears, and above it a substance enters a supercritical state that can transition between liquid-like and gas-like behavior without a phase change.
Charles Cagniard de la Tour first discovered the critical point in 1822 while working with carbon dioxide. The concept was later named by Dmitri Mendeleev in 1860 and independently by Thomas Andrews in 1869.
The critical point of water occurs at 647.096 kelvin and 22.064 megapascals. Above this temperature and pressure, water exists as a supercritical fluid and cannot be separated into distinct liquid and vapor phases.
Near the critical point, water shifts from nearly incompressible to compressible, loses its high dielectric constant, becomes a poor solvent for electrolytes, and mixes more readily with nonpolar gases and organic molecules. Every major property under normal conditions reverses near the critical point.
A supercritical fluid is a state of matter that exists above the critical temperature and critical pressure of a substance. It is continuously connected to both the liquid and gaseous states, meaning it can be transformed into either without undergoing a phase transition.
The Fisher-Widom line is a pressure-temperature line identified by Fisher and Widom that separates states with different asymptotic statistical properties above the critical point. Their work challenged the textbook claim that all distinction between liquid and vapor disappears entirely beyond the critical point.