What is the Mohs hardness scale and how is it useful for identifying minerals?

Mohs scale is a list of ten minerals. Each one has its own conventional degree of hardness and is one point harder then the next one. Here it is the scale:

As you've already noticed the scale is conventional. For example diamond has 10 points, but in fact it means that diamond is just harder then corundum which has 9 points. The digits are conventional. Modern technologies allow to define exact values for a mineral hardness. But usually for these kinds of measurements precise, expensive and usually not mobile equipment is necessary. Besides it's not necessarily to know precise hardness value to define a mineral. This makes instrumental measurement impossible and needles in field research. That's why the Mohs scale is so useful.

I think it's quite impossible to define a mineral using just its hardness value. Except you're trying to define very hard corundum or diamond which have no analogue. To define the mineral you have to know as mush as possible chemical and physical properties of the unknown mineral.