First let me say that homeownership brings enough with it without having to worry about the mechanical parts. Unfortunately, no one in the buying process sits you down for an education on the workings of the heating system.  Most of the time they are quite simple, however in the case of a heat pump, (air source which is most common) there are things that you need to know.  In fact on my first call to a heat pump owner, I generally give them this short little infomercial about how they operate. Most of them are appreciative to know how they work so... here is that class. The first thing you need to know is that a heat pump system is like two integrated heating systems in one.  For us in the north at least.  The first thing that happens is a call from the thermostat for first stage heat which is the heat pump. Now depending on the temperature, this will try to satisfy that call for heat.  If it cannot because of the outside temperature or the heat loss being too great it will, after a one degree drop in temperature, call for second stage heat which is in most cases an electric strip heater. Similar to a toaster oven element. This is usually when it starts to blow much warmer air and this then satisfies the thermostat until the next call for heat.  That is when the whole process starts over.  One of the big myths that homeowners go for is the setback thermostats will save you money.  This is true if you have a system that is not an air source heat pump. A heat pump has to run for a long time to add enough heat for the house and as the temperature drops outside, the heat pump produces less heat. This is why it needs a backup system.  The electric strip heaters are that back up system.  A setback thermostat attempts to drop the temperature for a specified amount of time and then suddenly brings the temperature up at a specific time. When the thermostat jumps up two degrees or more it skips right to the electric strip heaters bypassing the efficient heat that comes from the heat pump.  One other part about heat pumps is that the thermostat often has both auxillary heat and emergency heat which are both confusing to homeowners and often give the wrong impression.  Auxillary heat is simply the same strip heaters working as a backup after the heat pump could not get the job done.  However, when you set the thermostat to emergency heat, it bypasses the running of the heat pump altogether and goes straight to the electric backup.  Note: When the outdoor temperature is below 20 degrees you may as well set the thermostat to emergency if it is not setup to automatically do that, because at the temperature you are using more energy between the defrost cycles and running the heat pump than you would to just skip it and turn on the electric back up. But you will want to remember to turn the thermostat back to normal heat after it gets above 20 degrees again.  The most common complaint with a heat pump is that they blow cold air for a long time.  This is not technically true, but practically true, meaning the air temperature feels cold because it could be as cool as 75 to 80 degrees which certainly feels cold but technically is warm.  Since you are only adding a small amount of heat to the house at a time at the lower temperatures a heat pump will run a very long time.
That is another complaint I get often especially when homeowners have grown up in a gas furnace heated home. It seems to run all the time. While this is not technically true again, it seems to them to be the case.  The fact is that in order for heat pumps to do their job, they must run a long time. This does not mean that they are using more energy.  Actually what uses more energy is to skip the heat pump running and turn on the strip heaters. Those will make your electric meter spin really fast. The heat pump is basically an air conditioner in reverse. Taking the heat from outside and bringing it inside. Even though there is not as much heat outside in the winter, a heat pump can use what is there down to a specific point. One more thing to keep in mind, keeping the thermostat at a constant level is the most effective way to use a heat pump.  If you are constantly turning it up and down, you will be going in and out of auxillary heat instead of just using the heat pump. 
    As a side note: I personally like installing what I call a hybrid sytem. What that is- is a heat pump with a gas furnace as a back up. That way you get the efficiency with a less expensive backup. Of course everyone doesn't have that as an option if you do not have natural gas.

These are my thoughts and small educational quips. If you live in the North Indy area or anywhere in the Anderson area, I am a professional heating and air conditioning contractor that can service your system. My company is McConnell Plumbing, Heating, & Air Conditioning.