A surface whose metric
is equivalent to the metric of a plane. In other words, a surface that can be flattened without stretching.
A cylinder and a cone are developable, a sphere isn't. It can be proved that a surface is developable at a point iff its Gaussian curvature at that point is zero.
The fact that a sphere is not developable may be at the root of the earliest developments of topology and modern topography, at least as far as map-making is concerned.