Toughness is a measure of a material’s ability to resist fracture by absorbing the stress and strain imposed by sudden loading/impact. It tends to improve with increasing temperature.
Tough material may undergo some deformation in absorbing sudden impacts, and a very tough material will have high strength (ability to resist deformation) and high ductility (ability to change shape without failure). Toughness is the opposite of brittleness.
Hardness defines a material’s ability to resist permanent deformation or changes to its shape when under load, or to resist cutting, scratching or other forms of abrasion. So in general, the harder a material the greater its wear resistance. And for more detail click and see wikipedia entry.