The correct answer is: d) distribution of electrons among the bonded particles in a compound.
a) charge on an ion is only one specific aspect of oxidation numbers, while they can also be used for neutral compounds.
b) number of atoms or ions in a compound is a different concept entirely, unrelated to oxidation states.
c) type of bond holding particles together in a compound can be related to oxidation states, but it's not the primary purpose.
d) distribution of electrons among the bonded particles in a compound is the core function of oxidation numbers. They represent the hypothetical charge an atom would have if all its bonds were purely ionic. This helps track the electron transfer in chemical reactions and understand the electronegativity differences between atoms.
Therefore, option d) is the most accurate description of what oxidation numbers indicate.