The following picture (slide 4 from this presentation) qualitatively explains what is stated by Jeff Jupp (and I suspect that a very similar picture is used also in his paper):
The airfoil at the top is a "standard" one, while the one on the bottom is a supercritical one. Let's concentrate on the $C_p$ plots for the upper surface at the right of the figure.
As usual, the $C_p$ increases from the leading edge till (more or less) the thicker part of the airfoil and afterwards decreases till the trailing edge. The decreasing part of the $C_p$ is the most critical because there the boundary layer becomes very susceptible to any external perturbation. And this is exactly what is seen in the upper plot for the standard airfoil: after a peak there's a sudden drop in $C_p$ corresponding to the detachment of the boundary layer (in this case the external perturbation causing the detachment is a shock wave).
In a supercritical airfoil the angle of the aft portion of the airfoil "is reduced significantly, almost to zero" in order to smooth as much as possible out the decrease of $C_p$: its variation is now "spread" over a bigger portion of the upper aft surface, as visible for the supercritical airfoil at the bottom. That the $C_p$ remains more constant and higher on a bigger portion on the aft airfoil "increases the rear loading without increasing top surface pressure gradients".
This spreading of the aerodynamic loading toward the back of the airfoil has some important consequences, some of them also highlighted by Jeff Jupp like, on the negative side, the higher "weight of the flaps and the other secondary structure at the rear of the wing"; but, on the positive side, retarding as much as possible the drop of the pressure coefficient retards both the detachment of the boundary layer and the generation of a strong shock wave at transonic speeds, which is why supercritical airfoils have been introduced in the first place.