The coefficient of performance of a heat pump is COP = TH/(TH - TC), where TH is the temperature of the hot reservoir and TC is the temperature of the cold reservoir. The required power P is proportional to 1/COP, or to (TH - TC)/TH. If TH - TC is not too large then the required power P is also proportional to TH - Tc, because no insulation is perfect and hence heat will flow from the hot reservoir to the cold one, at a rate proportional to TH - TC if TH - TC is not too large. Thus, all told, if TH - TC is not too large, then P is proportional to (TH - TC)2/TH.
In simpler terms: As the outside air temperature increases or decreases relative to the desired inside temperature, the efficiency of air source heat pumps will decrease. Air source heat pump efficiency will be lowest when the outside temperature is either very high or very low, relative to the indoor temperature. This is important when considering the impact of air coupled cooling or heating on electric demand. Typically, these devices will produce the largest energy demand at times when electricity demand is already peaking. In fact, it is air-source heat pumps and air-conditioners that are a primary cause of energy peak demand during hot periods.
The efficiency of geothermal or water source heat pumps is much less impacted by the outside air temperature since such systems are not coupled to the outside air but rather to the ground or water which will typically have a temperature much closer to the desired indoor temperature.
think of the heat pump as a hydraulic device that pumps heat from a source (lowered) to a sink (elevated). If the difference (hight difference) between both is low, the work needed is also low.