To a Chemist A Mole Is An Avogadro
When chemists prepare a chemical reaction, they use moles, not grams, not cubic centimeters and not individual atoms. Chemistry existed long before the atomic theory was accepted. The word mole itself was only introduced around 1900, quite late in the game, by Wilhelm Ostwald. It was to mean a large number (of molecules) and was derived from the Latin moles, mass. A molecule, in fact, already meant a little mole. A bit later, in 1908, Jean Perrin proposed the name Avogadro's Number, denoted NA, to mean a mole. The precise value of NA is not specified, it has to be measured. The modern definition is the number of atoms of carbon in 12 grams of 12C (a single isotope of carbon). That number turns out to be around 6.0221367x1023 and it is still being actively investigated.
The need to consider a fixed number of atoms of a substance rather than a fixed mass or volume is rather obvious if you accept the atomic theory: atoms react together in simple ratios. For example, two atoms of hydrogen and one of oxygen react to form one molecule of water. But the atomic theory is what we are interested in proving, so we can't go that way.
Avogadro was being recognized posthumously for providing the key insight that convinced most chemists of the correctness of the atomic theory, and that insight had much to do with finding the correct counting rules.
Amedeo Avogadro (1776-1856)
In 1811 Avogadro  saw what Dalton and Gay-Lussac could not see. Dalton had postulated that molecules of simple gases such as oxygen and hydrogen were made of single atoms, something that was really beyond the hypotheses of his atomic theory and had more to do with his ideas about chemical bonds. Avogadro realized  that if (2) were wrong, and if instead molecules of simple gases were made of 2 atoms, then
would be consistent with both Gay-Lussac and Dalton's Law. He therefore conjectured that: (a) molecules of simple gases are di-atomic, and (b) at equal temperature and pressure equal volumes of gases contain equal numbers of molecules. The second conjecture being simply a restatement of Gay-Lussac's results in terms of Dalton's atoms, something now made possible by his first conjecture.2H2 + 02 -> 2H20 (3)
Avogadro was not well known and without a theory of molecular bonding his first hypothesis was hard to accept. It took another 50 years for chemists to reconcile all that was known of the chemistry of solids, liquids and gases within the atomic theory, and realize that Avogadro had been right from the beginning (Cannizaro, 1858 ).
Avogadro's Number is not important to the traditional chemistry of the elements (moles are) and it is not important to understanding atomic properties. But NA is key to undertsanding how the properties of atoms and molecules scale to the chemistry of the elements.
 Joseph Louis Gay-Lussac, Chemical Heritage Foundation.