Elastic potential energy
Elastic potential energy is the energy stored in the form of a reversible deformation of an elastic object.
The spring stores the energy used to extend it. The potential energy is thus given by the work $$(W)$$ done in deforming the elastic object.
The elastic potential energy of the stretched bow of an archer corresponds to the work done by the archer in stretching the bow.
The potential energy is converted into kinetic energy (movement) as the spring returns to its equilibrium (i.e. unstretched) state.
The elastic potential energy is the mechanical equivalent of the potential of the gravitational field. Both are relative quantities: we only measure differences in potential.
In the mechanical case, the reference potential is taken to be zero (i.e. at zero displacement).