The checklist procedure is:
Electric fuel pump ............. on
Mixture ............. rich
MAP ............. 15 in of Hg
RPM ............. 2300
Why the AFM says to turn on fuel pump during descent and not during climb?
AFAIK, every low-wing plane requires the boost pump to be on during takeoff, climb, descent and landing.
This is a safety measure. When you are flying low and slow, the consequences of the engine-driven fuel pump failing can be dire, so the added safety is worth a bit of extra wear on the boost pump.
During taxi, you want the boost pump off so you can detect a failure of the engine-driven pump while you’re still safely on the ground.
During cruise, you have sufficient altitude to safely turn off the boost pump and reduce wear. If the engine-driven pump fails, there is plenty of time to switch the boost pump back on and restart the engine; it may even restart on its own due to the prop windmilling.
High-wing planes generally don’t require running the boost pump (if they even have one) during these phases because gravity feed is a sufficient backup.
The previous answer stating that it is standard procedure on a low-wing aircraft to turn the electric/aux fuel pump on for takeoff for safety and to turn it on for descent to prevent vapor lock during low power settings is correct.
Diamond has a bit more to say about it. Diamond's descent checklist and climb checklist both call for the electric fuel pump to be turned on to pressurize the fuel to prevent vapor lock at high altitudes.
From the Diamond DA40 Aircraft Flight Manual Normal Operating Procedures Page 4A-32:
Item #4 Electrical Fuel Pump............ ON at high altitudes
CAUTION: Operation at high altitudes with the electrical fuel pump OFF may cause vapor bubbles, resulting in intermittent low fuel pressure indications, sometimes followed by high fuel flow indications."
Item #8 Electrical Fuel Pump............ ON at high altitudes
CAUTION: Operation at high altitudes with the electrical fuel pump OFF may cause vapor bubbles, resulting in intermittent low fuel pressure indications, sometimes followed by high fuel flow indications.
Unless you just took off from a high altitude airport, you are not usually at a high altitude when you are turning the electric fuel pump off during the climb check. When you start descent you often are at a high altitude, so according to Diamond you would turn the fuel pump on.
The most likely reason is, that during climb, the engine will, of course be running on high revs, and so will the engine's mechanical pump. It will most likely also be operating at better efficiency. For the fuel system & engine combination in question, the engines own fuel pump is not able to ensure sufficient fuel flow (unwanted lean condition) or pressure (possibility of vapor lock) to the engine at low revs, the descent attitude may also be a factor, so the electric pump is used as a backup.
General rule in aviation is, that if a system is not necessary for the safe operation of the aircraft, it is not used to save energy and the system from wear. This does lead to a lot of switch flicking...