The atomic number is the number of protons in the nucleus of an atom, according to M.J. Farabee, author of Chemistry 1: Atoms and Molecules. The number of protons define the identity of an element, and it determines how many electrons surround the nucleus. It is the arrangement of these electrons that determines most of the chemical behavior of an element.
In a periodic table arranged in order of increasing atomic number, elements having similar chemical properties naturally line up in the same column or group. For instance, all of the elements in Group 1A are relatively soft metals, react violently with water, and form 1+ charges; all of the elements in Group 8A are unreactive, monatomic gases at room temperature. In other words, there is a periodic repetition of the properties of the chemical elements with increasing mass.
In the original periodic table published by Dimitri Mendeleev in 1869, the elements were arranged according to increasing atomic mass. At that time, the nucleus had not yet been discovered, and there was no understanding at all of the interior structure of the atom; therefore, atomic mass was the only guide to use. Once the structure of the nucleus was understood, it became clear that it was the atomic number that governed the properties of the elements.