Illustration of tensile strain.
A spring constant tells how difficult a spring is to stretch or compress, now many Newtons of force are required per meter of deformation. The higher the spring constant the stronger the spring.
In the discipline of elasticity, or 'mechanical properties', a quantity called the elastic modulus is central to the discussion. The elastic modulus tells you how much stress is required to produce a given strain (tensile, sheer, or bulk).
The elastic modulus provides the same kind of information about a solid body for a variety of different kinds of deformations that a spring constant provides about a spring. For the one dimensional deformation of a spring, the spring constant tells how much force (stress) is required to produce a certain amount of displacement on the spring (strain).
In fact, the more general elastic modulus relationship itself can be simply referred to as Hooke's Law. Hooke's Law for springs is a simple, model case of the more general relationship that Hooke expressed in the 17th century, 'As the extension, so the force.'