Hardness of a gemstone is one of the components that defines the durability of gemstones. (Other components are toughness, brittleness and stability - resistance to heat and/or chemicals.) In gemology, we define hardness as the ability to withstand abrasion by other materials.
Mohs hardness scale
In the early 19th century, Friedrich Mohs developed a scale of relative hardness for minerals. He composed a list of 10 minerals with known hardness and organized them on an ascending scale, with talc at the lower end and diamond at the highest end.
It should be noted that this is not a linear scale. The difference in actual hardness between diamond and corundum is 10 times higher than the difference between talc and corundum [Read, 2005]. Thus it is a comparative hardness scale, with the hardness of one mineral relative to another mineral on the list.
As can be seen in the list, quartz has a hardness of 7 on Mohs scale. Quartz is one of the most abundant minerals on Earth and is even in dust particles that constantly float through the air. This is why minerals with a hardness less than 7 will abrade relatively rapidly with normal wear.
Of course, all minerals could be put on the scale, but that would create an almost endless list.
The method of testing the hardness of gemstones is by the use of hardness pencils.
Hardness pencils are pencils with a tip made of one of the 10 minerals on Mohs scale.
These pencils are used to try and scratch a stone and observe if the pencils can scratch the gem. Since this is a destructive method (it leaves a scratch), this test is mostly used on pieces of rough or on a inconspicuous place on the gemstone. Not many gemologists use this test as there are better ways to determine a gemstone's identity.
When one does feel the need to apply this test, one must do it in a logical manner.
The gemstone is tested with a pencil of low hardness (starting at 4 or lower) to try to put a tiny scratch on the stone without applying pressure. If no scratch is observed, one repeats this process with a pencil of higher hardness (in this case 5) and so on until one arrives at the pencil that is able to put a tiny scratch on the stone.
For instance, if one could not scratch the mineral with pencil no.7 but it would leave a scratch with pencil no.8, the hardness of the mineral must be between 7 and 8 on Mohs scale.
Due to various causes, some minerals are harder in one direction than in another direction. Kyanite has a hardness of 5 in the basal plane direction, while it has a hardness of 7 in the prismatic directions. This phenomenon of varying hardness in different directions is named "directional hardness".
Diamond also has a profound directional hardness. Diamond is softer in the octahedral planes and harder in the cubic planes (and even softer in the dodecahedral planes). This property helps the diamond cutter, because diamond dust (which is orientated in a random fashion) will always have part of the dust aligned in its hardest direction, so it can easily be used to saw and polish in the octahedral direction of a to-be-cut diamond.
Directional hardness is also named "differential hardness".