Refer to figure.
The figure shows the power required vs airspeed. This is the amount of engine power that is required to overcome the drag for different speeds, flying straight-and-level. The power required curve is very similar to the thrust required curve (also shown), where Power = Thrust x TAS.

For a piston engine aeroplane, the amount of power produced by the engine is directly linked to the fuel flow. Maximum endurance means flying such that the fuel flow is lowest (so that the fuel will last for as long as possible). This means flying at a speed where the power required to maintain flight is the lowest possible.

Referring to the figure, this corresponds to the point A. The airspeed that corresponds to minimum power required is known as V_MP (Minimum power speed) and this is the speed for best endurance in piston engine aeroplanes.

Note: Don't confuse this curve with the thrust required curve, which looks very similar. the minimum point on the thrust required curve is V_MD which for a piston engined aeroplane is the speed for best range not best endurance.