Mole is simply a measure of a number of particles, as is a dozen. Where a dozen eggs means 12 eggs, that is a single box of eggs, a mol simply means 6.022 x 10²³ particles, usually atoms or isotopes. Therefore:

1 mol = 6.022 x 10²³ atoms, isotopes, ions, molecules or whatever

This number is the Avogadro constant. As atoms, isotopes or ions of different elements have different numbers of neutrons, protons and electrons, they have different weights (masses). Therefore, equal numbers of atoms or isotopes of different elements or isotopes have different weights (masses). The weight (mass) per mol of an element or isotope is its atomic weight or molar weight (atomic mass, molar mass). This means for example:

1 mol ⁴⁰Ar = 6.022 x 10^{23 40}Ar atoms have a mass of 39.962 grams, therefore the atomic or molar weight of ⁴⁰Ar is 39.962 grams/mol.

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As elements are usually mixtures of different isotopes, the molar mass of an element gives the averaged molar masses of the isotopes weighted by their isotope abundances. Watch this example:

Potassium: K: Molar mass = 39.0983 grams/mol

This calculates from the masses of all K-isotopes and their isotope abundances:

³⁹K: atomic mass = 38.9637 amu, present day abundance = 93.2581%
⁴⁰K: atomic mass = 39.9640 amu, present day abundance = 0.0117%
⁴¹K: atomic mass = 40.9618 amu, present day abundance = 6.7302%

Therefore, the molar mass of K can be calculated as follows:

38.9637 x 0.932581 + 39.9640 x 0.000117 + 40.9618 x 0.067302

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Information about the elements, including isotope abundances and masses, can be found here.