The Mole was initially hypothesized by Italian physicist Amedeo Avogadro in 1811. Specifically, Avogadro believed that equal volumes of different gases at the same temperature would have the same number of molecules. Avogadro's hypothesis was not yet a constant used for calculation of measurement; rather, it was a concept of molecular/atomic measurement that would later be refined and developed by many more scientists such as Stanislao Cannizzaro and Albert Einstein. The mole was found to be precisely 6.022 x 10^23, and dubbed "Avogadro's Number".
The mole's significance in chemistry is irreplaceable-- other quantities such as the dozen (12), ream (500), or century (100) are much too small to measure particles. The mole gives a visible, reasonable measurement for the scientist to work with. In addition, 1 mole of an element weighs the same as that element's atomic mass (in grams). This makes for easy conversions and calculations.
Sources:
http://www.chemicalformula.org/chemistry-help/mole-chemistry
http://iopscience.iop.org/0026-1394/31/3/001
http://www.visionlearning.com/library/module_viewer.php?mid=53
