Curvature is the reciprocal of radius of curvature. The units are 1/L or L-1 where L represents length. In the imperial system, curvature would be measured in ft-1 or in-1.
Curvature of a structural member is closely approximated by the expression M/EI. A dimensional analysis shows that the units turn out to be "#/(#/in2*in4) or in-1.
If you plot the M/EI diagram for a structural beam, you are plotting curvature from end to end of beam. In the case of a uniformly loaded beam, moment is a parabola. If EI is constant over the span, then M/EI is also a parabola. The rotation between any two points on the beam is the area under the M/EI curve between the two points.
A simple beam loaded with an equal and opposite moment at each end has a constant moment across the span, hence constant curvature. That is cylindrical bending. The change in rotation from one end to the other is the area under the M/EI curve, namely ML/EI where L is the span. By symmetry, the rotation is equal in magnitude at each support, so the rotation at each end is ML/2EI.
Rotations for other types of loading can be worked out in similar fashion. Sometimes the geometry gets a bit messy, but the concept is straight forward. The conjugate beam method is an easy way to determine slopes and deflections of simple span beams and I recommend you check that out using Google.
BA
