A heat pump system is an energy-efficient way to heat and cool your home year-round. It is a type of air conditioning that is capable of working in reverse during the cold months. During the summer months, your AC system pulls heat out of the house, allowing super-cooled air to take the place of the heat. In the winter, the heat pump pulls heat out of the atmosphere (yes, even in the dead of winter, heat is present in the air) and delivers it to the interior.
A split system is where one component – the condenser/compressor unit – resides outside the home on a slab, flat roof or landing, while the other component – the air handler/evaporator coil – resides inside the house. This is a very common configuration and can pretty much be considered the norm for family homes in the US.
To put it simply, a central air and heat pump system is an air conditioning system that also works in reverse to heat your home in the winter.