Here is a video about phase diagrams (13min): Phase Diagrams, by Khan Academy, on YouTube
You know that phase changes usually depend on temperature, which
determines the kinetic energy of atoms and molecules. We mentioned
before that they also depend on pressure. In the section on phase changes we said that the boiling
point is the place where vapor
pressure is the same at the external pressure, so clearly boiling
point depends on pressure! Melting temperature also depends on pressure (usually
the density of solid and liquid are different, so it makes sense) but
not nearly as much as boiling point, since the volume changes are
smaller. We use phase diagrams to show how the
transition temperatures depend on temperature and pressure both.
The second red point in the diagram is the critical point. The dotted black lines show the area where a supercritical fluid exists. This is the high-temperature, high-pressure part of the diagram. Because the temperature is high, the molecules have lots of kinetic energy, so a liquid form isn't really stable because the intermolecular forces aren't strong enough to hold such energetic molecules together. However, the pressure is so high that the molecules can't really get away from each other either, so they bump into each other a lot, and feel some attractions, and don't really act like a normal gas (certainly not an ideal gas!). Past the critical point, there's no distinct liquid or gas, just a supercritical fluid with some special properties.
Supercritical fluids can make good solvents. For instance, supercritical CO2 is commonly used because it is a safe, inert, inexpensive non-polar solvent. Most non-polar solvents are not very safe (toxic and flammable), and disposing of them is expensive; supercritical CO2 avoids these problems.