In classical differential geometry, development is the rolling one smooth surface over another in Euclidean space.
For example, the tangent plane to a surface (such as the sphere or the cylinder) at a point can be rolled around the surface to obtain the tangent plane at other points.
Differently put, the correspondence provides an isometry, locally, between the two surfaces.
Perhaps the most famous example is the development of conformally flat n-manifolds, in which the model-space is the n-sphere.
The development of a conformally flat manifold is a conformal local diffeomorphism from the universal cover of the manifold to the n-sphere.