A test-specific measure of a material's resistance to mechanical penetration (indentation) of its surface. All hardness values are reported as belonging to some hardness scale. Some of the most popular scales are Brinell, Knoop, Rockwell, Shore, and Vickers.
The Brinell test uses a spherical indenter, which can be made from one of a number of materials, depending on what is needed to indent the sample without deformation to the indenter. The Knoop test uses a small diamond pyramid indenter, and can be used on very thin and very brittle materials.
The Rockwell test is very easy to apply (hence its popularity, particularly with metals), but any given testing configuration will only produce meaningful results for a narrow range of hardnesses. A particular testing configuration is most commonly declared with a latter (e.g. B, C, F, or R).
The Shore test (also called Durometer hardness, after the device used to take the measurement) is specific to rubbers and soft plastics. As with Rockwell, different testing configurations are standardized as separate, and non-interchangeable, scales. By far the most common Shore hardness scales are A and D.