The scale used to measure the hardness of minerals is the Mohs scale. This scale rates minerals from 1 to 10 based on their ability to scratch one another, with talc being the softest at 1 and diamond being the hardest at 10. The classification helps in identifying minerals and understanding their properties. Each mineral's hardness is crucial in applications like jewelry, manufacturing, and geology, as it influences their durability and suitability for various uses.