An Ion is an atom that has more or less electrons than protons or a Neutral Atom, in which they match, and the term State of Ionization is used to characterize this difference, e.g., "missing two electrons". The term is also used regarding the degree of ionization of a material (collection of atoms/ions) or simply to state that an atom is ionized.
For a collection of atoms, e.g., a gas, the percentages of the gas at each state of ionization is of interest, because of its relation to Temperature and to the production of the Spectral Lines, allowing the study of spectral lines to be used to determine temperature, through the Saha Equation.
In astronomy, the following terminology is often used: the chemical symbol followed by I means neutral, II means singly ionized, III for doubly ionized, etc., e.g., CI, CII, CIII for Carbon (C) at these three states of ionization. The more common symbol in other sciences is (e.g., for Hydrogen (H)), H+ for singly ionized, H++ for doubly ionized, etc.