To get a clear picture of what is happening you have to first look at the entire system from the source of pressure to the discharge point, and then look at the section from the valve to the discharge point.
To keep things simple let us assume that the source of pressure is constant. As you change the valve position the pressure drop across the valve will change (as described by the calculator referenced by Breizh). Since the source pressure is constant, if the pressure drop across the valve changes then the pressure drop across the rest of the line must change to compensate. For example, if you open the valve the pressure drop across it will reduce, but the flow rate will increase and therefore the pressure drop through the rest of the line will increase so that the overall pressure drop remains constant.
The section from the valve to the discharge point will not have changed physically, but the flow rate will have increased so the pressure drop also increases. So opening the valve raises the downstream pressure and closing the valve lowers the downstream pressure. The simplistic way to look at it is to say that with the valve opening more it is allowing more of the pressure to pass through to the downstream side, but this is not correct. The real reason is the change in flow rate as described above and the resulting pressure drop across each section.