Avogadro’s Number itself is roughly 6.022×10^23, and if you have this many of something, you have a “mole” of that thing. Why this matters, is that the mass of a mole of something, measured in grams, is the same as the mass of one of that thing, measured in atomic mass units (essentially the average mass of a proton and a neutron). So a mole of carbon-12 (six protons, six neutrons, six electrons which are about 2000 times lighter than either of the other) has a mass of 12 grams. This makes for a useful conversion in chemistry, since you know how to get the same count of molecules of two different substances when mixing them, just by totaling their respective atomic masses.
Using Avogadro’s number is deprecated in favor of Avogadro’s constant, which is a more precise number expressed as a conversion 6.022140857×10^23 / mol.
Avogadro’s number was named for Amedeo Avogadro, by French physicist Jean Baptiste Perrin. Avogadro was an early 19th century Italian physicist. He briefly held a professorship in the University of Turin before being relieved of it as a consequence of joining the revolutionary movement during the Piedmont insurrection (an early skirmish in Italian Unification) in 1821. He was restored to his chair in 1833 and taught for twenty more years.
Avogadro’s Number is a quantification of Avogadro’s Law, a principle of ideal gases that builds on the work of Gay-Lussac in understanding the volume/temperature/pressure relation of gas mixtures. Avogadro discovered that the ratio of molecular masses between two gases mirrored the ratio between the constants resolving each gas’s P*V/T equation. This further helped understanding the distinction between atoms and molecules, and eventually the ideal gas equation P*V = n*R*T, where n is the number of molecules in the quantity of gas, and R is a universal conversion constant.