Supercritical gas, more correctly known as supercritical fluid, is a distinct state of matter that has properties of both a liquid and a gas. A supercritical gas may be regarded as an intermediary state between liquids and gases. Supercritical gases are only created above a material's thermodynamic critical point. This usually means high pressures, often between about 40 and 80 atmospheres, though it varies greatly. Some critical points, most notably water, are as high as 218 atmospheres and beyond. Supercritical fluids have low viscosities and high diffusivities.
Supercritical gases can diffuse into and through solids like a gas, but also dissolves certain materials like a liquid. Supercritical fluids are found in at least two areas of nature. The first is around hydrothermal vents and submarine volcanoes on the ocean floor, where the pressure is so great that the creation of a supercritical gas is possible. The pressure 3 km (1.8 mi) underwater is 300 atmospheres, more than enough. Another natural supercritical gas is the lower atmosphere of Venus, which is very dense and hot (93 atmospheres, 735 K) at the surface. Oddly enough, this means that only two states of matter can be found on the surface: solid and supercritical gas. Conventional liquids and gases do not exist there.
Supercritical fluids have at least a dozen industrial applications. One is supercritical fluid extraction, where supercritical fluids are used to extract some material from a surrounding matrix. This is used to extract caffeine from coffee beans. Supercritical carbon dioxide sucks the caffeine right out of them. Similarly, supercritical fluids are used in supercritical drying, which extracts a liquid from a matrix. This is used in the preparation of biological samples for electron microscopy, as well as the synthesis of aerogel, a material which holds 12 Guinness World Records for properties such as lightness and insulation.
Supercritical water oxidation is used to oxidize hazardous wastes, making them safe for disposal. The process is also used to synthesize micro and nano-particles for various pharmaceutical applications. The reverse of supercritical fluid extraction is called impregnation, whereby a material is introduced to a matrix rather than removed. The list goes on. As you can see, the applications of supercritical fluids are numerous.