The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law:
Young's modulus describes the material's response to linear stress (like pulling on the ends of a wire or putting a weight on top of a column), the bulk modulus describes the material's response to uniform pressure (like the pressure at the bottom of the ocean or a deep swimming pool) the shear modulus describes the material's response to shear stress (like cutting it with dull scissors).
The shear modulus is concerned with the deformation of a solid when it experiences a force parallel to one of its surfaces while its opposite face experiences an opposing force (such as friction). In the case of an object that's shaped like a rectangular prism, it will deform into a parallelepiped. Anisotropic materials such as wood, paper and also essentially all single crystals exhibit differing material response to stress or strain when tested in different directions. In this case one may need to use the full tensor-expression of the elastic constants, rather than a single scalar value.
One possible definition of a fluid is material with zero shear modulus. As found on Wikipedia, to be checked. Please contact us if you would like to contribute.