HSPF stands for Heating Seasonal Performance Factor. It is a measure defined by the Air Conditioning, Heating, and Refrigeration Institute to rate the heating efficiency of air conditioner or heat pump. Let me emphasis that again, the HSFP rating only reflects the heating efficiency of a heat pump, not its cooling efficiency. Cooling efficiency is rated using a different metric called SEER. See this post for more information about SEER.
The efficiency of a heat pump is highest when the difference between the indoor and outdoor temperature is the least. For this reason, air-source heat pumps are much more efficient in the spring and fall then in the winter and summer. The HSPF rating attempts to take seasonal variations in heat pump efficiency into account. For this reason, it can be thought of as an average heating efficiency over the course of a year.
HSPF is defined as the ratio of the thermal energy transferred into your home per heating season in British thermal units (BTU) divided by the electrical energy consumed by the heat pump in watt-hours (Wh) per heating season. More compactly,
HSPF = (thermal energy transfered, BTU)/(electrical energy used, Wh)
As a physicist, it doesn’t make much sense to mix two units of energy (BTU and Wh) in the same formula. It makes understanding the formula more complicated. If one notes that
1 Wh = 3.412 BTU, then
HSPF = 3.412 (thermal energy transfered)/(electrical energy used)
where the energies can be in any units so long as they are the same units. In this form, you can see that a 100% efficient electric resistive heater has a HSPF rating of 3.412. Thus a heat pump with a HSPF rating of 6.8 would pump about twice as much thermal energy into your home as it consumes in electricity.
Although the HSPF rating you will actual achieve depends on your climate (hotter climates will achieve higher real-life HSPF ratings than cooler climates) replacing a 6 HSPF heat pump with a 9 HSPF heat pump will decrease the amount of electricity needed to heat your home by about 33.3%. In general, you can calculate the percent reduction in electricity used by a new heat pump to heat your home using the following formula.
Percent Energy Savings = 1 - (Old System HSPF)/(New System HSPF)