Consider applying an external voltage to the junction as shown below, with the negative terminal connected to the P type material and the positive terminal connected to the N type material. If this was a simple conductor, the external voltage would cause electron flow from the negative terminal of the battery, through the device and back to the positive terminal. However for the PN junction this would require injecting electrons into the P type material. These electrons would recombine with holes and therefore further deplete the majority charge carriers in the P type semiconductor. Also, removing electrons from the N type material, would obviously cause further depletion of free electrons, (i.e. the majority charge carriers in the N type semiconductor). This causes a widening of the depletion layer and an increase in the charge at the junction, which reinforces the barrier voltage and opposes the applied voltage. The net result is that when the PN junction is reversed biased, it blocks current flow.
Another way of understanding this, is to consider the conduction properties of the depletion region. It is completely depleted of majority current carriers. i.e. The free electrons produced by the doping process in the N type material, have migrated across the junction and the majority carriers, (holes), in the P type have been lost, due to recombining with these electrons. Therefore the conduction properties within the depletion layer, have been reduced to that of pure silicon and so it forms a high resistance barrier, between the conductive material either side.
If the semiconductor was at a temperature of 0K, the depletion layer would act as a perfect insulator and no current would flow. However like pure semiconductor, at normal temperatures electron hole pair generation occurs, which provides enough mobile charge carriers for a small current to flow through the depletion layer. We refer to this as leakage current.
In summary, we can say that in a reverse biased PN junction, there is no current flow from majority charge carriers through the device, because there are no majority charge carriers within the depletion layer. However, a small leakage current will flow, due to minority charge carriers from electron hole pair generation. (The depletion layer effectively forms a very high resistance layer between the conductive regions, which only allows a small leakage current to flow.)