What is the role of HP (high pressure) and LP (low pressure) fuel pumps in aircraft like the A320? Why are two different ones needed?
The question asks about all low pressure fuel pumps on commercial aircraft but the diagram depicts only one specific instance (of a two stage high pressure pump) and is confusingly labeled.
The low pressure pumps move fuel around the aircraft where only volume is needed. These pump through comparatively large pipes with low back pressure, so they operate at less than 60psi. Fuel is used to maintain balance, reduce flutter susceptibility and for cooling in addition to providing an energy source for the engines. The a320 has six low pressure pumps serving the center and inside fuel tanks. A series of valves control where fuel goes. The outer tanks gravity feed the inner tanks, so no pumps are needed.
The high pressure pumps are attached to an engine and atomize fuel into a burnable spray inside the combustion chamber, where high pressure is needed to overcome combustion pressures as high as 600psi in modern engines. This nozzle test is at 200psi but in operation the pressure may be 1000psi or higher.
The high pressure pump typically consists of multiple stages as a single stage cannot achieve the desired pressure. Shown is a two stage high pressure pump with a low pressure centrifugal boost stage on the right followed by a high pressure gear stage to the left.
This matches the OP's diagram depicting a single mechanically driven engine fuel pump (in red) containing a centrifugal low pressure and geared high pressure 'pumps' (in yellow) more easily understood as stages.
In general LP pumps supply fuel to the engine from the fuel tank. HP pumps supply fuel to the injectors. This principle works not only for aircrafts but even on modern cars. It's sometimes possible for engine to work if other pump is not working but with less reliability usually if LP pump is broken. HP pump at the engine ensures that you don't need long lines to have high pressure. If you don't have LP pumps you can easily run into vapor bubble issues in the fuel line. If LP pump fails engine still can use suction feed from HP pump.