Hardness is a measure of how easily a mineral is scratched.

Mohs Scale of Hardness orders minerals from the softest (1 Talc) to the hardest (10 diamond). A mineral that has a specific hardness can scratch any mineral that has a lower hardness. The hardness scale is not linear. Quartz (hardness 7) is 100 times harder than talc and a diamond (hardness 10) is 1600 times harder than talc.

Hardness is not resistance to breaking. Diamonds are very hard, but they chip relatively easy. You can chip a diamond hitting it on a drinking glass, but the diamond will easily scratch the glass.

Specific Gravity
Specific gravity is covered under weight in the 4Cs.

Refractive Index
Refractive index is one of the main ways of identifying a gemstone. The refractive index (RI) is an optical property that is the ratio of the speed of light through a vacuum to the speed of light through a transparent medium. Light is bent as it moves from air into a transparent material. This effect can be seen when putting a straight rod half-way in water and the rod appears to be bent.

Gemstones with a higher refractive index tend to be more brilliant. Light is bent at a higher angle when it enters a cut gemstone with a higher refractive index and thus more light is reflected back out the top. For example diamond has a high refractive index.
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