According to the Bohr model of the atom, electrons exist in quantized energy levels surrounding the atom's nucleus. These energy levels are described by the angular momentum quantum number, n = 1, 2, 3, ... . Electrons may only exist in these states, and may only transition between these states. The set of trasitions from n ≥ 3 to n = 2 are called the Balmer series and are named sequentially by Greek letter: n = 3 to n = 2 is called H-alpha, 4 to 2 is H-beta, 5 to 2 is H-gamma, etc. For the Lyman series the naming convention is 2 to 1 is Lyman-alpha, 3 to 1 is Lyman-beta, etc.
H-alpha has a wavelength of 6563Å (6.563×10−7m; see angstrom) is visible in the red part of the electromagnetic spectrum, and is the easiest way for astronomers to trace the Hydrogen content of gas clouds.
In the Treaty of Armens, "unwanted lifeforms inhabiting H class worlds may be removed at the discretion of the Sheliak Corporate." (TNG: "The Ensigns of Command")
An H class planet or moon could contain an atmosphere consisting of Oxygen and Argon.
According to the Star Trek Star Charts, Class H worlds have an age of 4-10 billion years and have a diameter ranging from 8,000 to 15,000 km.