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A HI region (read as "H one region") is a cloud of generally neutral atomic hydrogen (HI), typically with on the order of 1 in 10,000 atoms ionized. Their typical temperature range is ~100 K, in which case the material is referred to as a cold neutral medium (CNM). Above that temperature, they are unstable, but are stable again above 10,000 K. Between those temperatures, they generally cool or heat to a stable state. They typically also have some helium and other elements. HI is not very luminous, mostly the 21-cm line, which along with the spectral lines of other elements embedded in the cloud, allows the clouds to be detected.
Other kinds of hydrogen clouds include HII regions and molecular clouds. HI regions and HII regions are termed diffuse clouds and molecular clouds (which are even cooler and more dense) are termed dense clouds.
The term HI region is generally used for such clouds within galaxies, which occur after some of the ISM has had a chance to cool. These are ubiquitous, but any clouds external to galaxies of HI are of high interest and terms for types of them have been coined such as intergalactic HI cloud and reionization-limited HI cloud (RELHIC).