An intuitive view of the Cp-curvature relation

For equilibrium we must have a pressure gradient when the flow is curved.

In the case shown here, the pressure must increase as we move further from the surface. This means that the surface pressure is lower than the pressures farther away. This is why the Cp is more negative in regions with curvature in this direction. The curvature of the streamlines determines the pressures and hence the net lift.