I will restrict my answer to common engineering materials from which useful objects could be fashioned, where hardness would be a useful attribute. This excludes metals that catch fire spontaneously in air, since it would be injudicious to make cars and airplanes out of them. Hardness is a measure of how difficult it is to indent a material

Hardness is a material's resistance to surface deformation. Harder surfaces are subjected to greater internal stresses, and have a tendency to increase in 

Hardness is the resistance of a material to localised plastic deformation. Hardness ranges from super hard materials such as diamond, boron-carbide to other ceramics and hard metals to soft metals and down to plastics and soft tissues.

The hardness of a material can be determined based on Moh's scale of hardness, which ranks a material based on a list of standard materials with known hardness. The hardness of the material is ranked on the scale between the material it just scratches and the material that it fails to scratch. Moh's Scale of hardness Indentation testing

Hardness is a metric that measures how resistant a material is to localised plastic deformation caused by mechanical indentation or abrasion. It has important diagnostic properties in mineral identification or abrasion. There is a general bounding between hardness and chemical composition, thus most hydrous minerals like halides, carbonates, sulfates, and phosphates

In materials science, hardness (antonym: softness) is a measure of the resistance to localized plastic deformation induced by either mechanical indentation 

The science of mechanics of materials aims to relate hardness to the more fundamental properties, such a modulus of elasticity, fracture strength, 

hard'nes ), 1. The degree of firmness of a solid, as determined by its resistance to deformation, scratching, or abrasion. See also: hardness scale, number. 2. The relative penetrating power of a beam of x-rays, used both within the diagnostic range of energy and in radiation therapy; expressed in terms of half-value layer.

Metal Properties: Hardness, Toughness, & Strength {Infographic} · Hardness: A material's ability to withstand friction, essentially abrasion 

Macroscopic hardness is generally characterized by strong intermolecular bonds. However, the behavior of solid materials under force is complex, resulting in 

Hardness is the surface property of a material that allows it to resist penetration of by another material. For example: a diamond is harder than steel,