A mole is simply a unit of measurement. Units are invented when existing units are inadequate. Chemical reactions often take place at levels where using grams wouldn't make sense, yet using absolute numbers of atoms/molecules/ions would be confusing, too.

Atomic weight—the average mass of the atoms of an element taking into account the masses of the various isotopes and their relative abundance. For example, oxygen has an atomic weight of 15.9994. This means that the average of the atoms’ masses is 15.9994 atomic mass units (amu).  

A mole is the quantity of anything that has the same number of particles found in 12.000 grams of carbon-12. That number of particles is Avogadro's Number, which is roughly 6.02x10²³.