Mole is equivalent to the Avogadro Number which has a value of 6.022×1023 elementary entities of the substance. Consider this example
2 H2 + O2 → 2 H2O implies that 2 mol of H2 and 1 mol of O2 react to form 2 mol of H2O.
Whereas Molarity is defined as the number of moles of solute dissolved in 1 liter of solution. Lets take an example:
We find molarity of a solution that contains 10.0g of HCl (molar mass 36.5g/mol) per liter of solution
Number of moles of HCl equivalent to 10.0g of HCl.
10.0g HCl × 1 mol HCl36.5g HCl = 0.274 mol HCl
With 0.274mol/lt the molarity is 0.274M in HCl.