Avogadro's number

The Avogadro constant (symbols: L, NA), also called the Avogadro number is the number of "entities" (usually, atoms or molecules) in one mole, that is the number of carbon-12 atoms in 12 grams (0.012 kg) of unbound carbon-12 in its ground state. The current best estimate of this number is :
NA = ( 6.02214179 ± 0.00000030 ) * 10^23 / mol

Before 1960, there were conflicting definitions of the mole, and hence of the Avogadro number (as it was known at the time), based on 16 grams of oxygen: physicists generally used oxygen-16 while chemists generally used the "naturally occurring" isotope ratio. Switching to 12 grams of carbon-12 as the basis ended this dispute and had other advantages.

At this time, the Avogadro number was defined as the number of atoms in 12 grams of carbon-12, that is as a dimensionless quantity, while a mole was defined as one Avogadro number of atoms, molecules or other entities. When the mole entered the International System of Units (SI) in 1971 as the base unit of amount of substance, the definitions were interchanged: what had previously been a number became a physical constant with the unit of reciprocal moles (mol^-1).

The Avogadro constant can be applied to any substance. It corresponds to the number of atoms or molecules needed to make up a mass equal to the substance's atomic or molecular mass, in grams. For example, the atomic mass of iron is 55.847 g/mol, so NA iron atoms (i.e. one mole of iron atoms) have a mass of 55.847 g. Conversely, 55.847 g of iron contains NA iron atoms. The Avogadro constant also enters into the definition of the unified atomic mass unit, u:

Additional physical relations
Because of its role as a scaling factor, the Avogadro number provides the link between a number of useful physical constants when moving between the atomic scale and the macroscopic scale. For example, it provides the relationship between:

the gas constant R and the Boltzmann constant kB:
R = kB * NA = 8.314472 ± 0.00000030 J mol^-1 K^-1
in J mol^-1 K^-1
the Faraday constant F and the elementary charge e:
F = NA * e = 96485.3383 ± 0.0083 C mol^-1
in C mol^-1

A number of methods can be used to measure the Avogadro constant. One modern method is to calculate the Avogadro constant from the density (ρ) of a crystal, the relative atomic mass (M), and the unit cell length (a) determined from x-ray crystallography. Very accurate values of these quantities for silicon have been measured at the National Institute of Standards and Technology (NIST) and used to obtain the value of the Avogadro constant:
NA = 4 M / (a^3 * ρ)
based on silicon.

I hope this can help your understanding. :)