A hydrogen atom is one proton with one electron bound to it. That is the whole thing. In the commonest isotope, protium, there is no neutron at all, which makes it the only atom whose nucleus is a single particle. About one hydrogen atom in 6,400 is deuterium, carrying one neutron; tritium, with two, is radioactive and decays with a half-life of a little over twelve years.
Because it is the simplest, it is the one atom whose behaviour can be solved exactly. The spectral lines of hydrogen, the ladder of frequencies it absorbs and emits, were measured before anyone could explain them, and fitting them is what forced quantum mechanics into existence: Johann Balmer's formula of 1885 was numerology until Niels Bohr's model of 1913 gave it a reason, and Erwin Schrodinger's equation of 1926 gave it a proper one. Every account of atomic structure since is an approximation to a problem that hydrogen alone poses cleanly.
Hydrogen is roughly three quarters of the ordinary matter in the universe by mass, and effectively all of it was made in the first few minutes after the Big Bang. Stars consume it: the proton-proton chain that powers the Sun fuses hydrogen into helium, and that reaction is the source of very nearly all the light that has ever fallen on the Earth.
On Earth free hydrogen is almost absent. The molecule is light enough to escape the atmosphere entirely, so what remains is bound: into water, which is a ninth hydrogen by mass, into every hydrocarbon, and into every protein and nucleic acid in every living thing. Hydrogen bonds, the weak attractions between a hydrogen atom and a nearby oxygen or nitrogen, hold the double helix together and give water its unreasonably high boiling point. Without that one small anomaly the planet would have no liquid oceans.