air-source heat pumps
Air source heat pumps are able to extract heat from the cold outside air, or the opposite.
Air source and ground-source heat pumps 
Instead of extracting the heat or the cold from the ground or the water - as geothermal heat pumps do - the much more common air-source heat pumps extract them from the outdoor air, and drives it into the house.
Image credit: Danfoss.
Central air-source heat pumps
Most air-source heat pumps are two-piece units. They comprise...
1 - An outdoor unit - looking like an air conditioner in size and appearance - usually consisting of an outdoor coil, a compressor, a reversing valve and a fan.
2 - An indoor unit, called the air handler, that looks like a gas furnace (though the system doesn't work or involve any furnace). The air handler contains a large blower and a filter just like conventional air conditioners.
In the case of central heat pumps the heated (or cooled) air is distributed around the house via ductwork (and the blower).
Ductless mini split heat pumps
In ductless heat pump systems there is only one outdoor unit but multiple indoor units. The term "mini" associated to these pumps describe the small indoor units located in each room or part of the house (articulated with the outdoor unit through a conduit system) where the final heated or cooled air is produced and blown.
For more details, see: Ductless mini split heat pumps.
Supplemental heater
The problem with air-source heat pumps is that they are unable to extract heat from outdoors air during freezing times. When temperatures drop below 0ºC/30ºF, the problem begins, and to surpass it a supplemental heater is needed (it may be turned on automatically).
Advantages of air heat pumps
Air heat pumps are emerging as a popular choice due to their simple ‘plug and play’ installation and competitive pricing. Air heat pumps are typically competitive with traditional electrical and fuel-based systems, though not so much with gas-powered appliances (see Are Heat Pumps Suitable for my home?
See also: Heat Pumps prices
Disadvantages of air-source heat pumps
Air source heat pumps perform better in mild temperate. In climates with extended periods of freezing temperatures, they force users to use electric or gas heaters...
Ground source heat pumps are more efficient, and can overcome the limitations of the air-source heat pumps. But their prices are much higher...