Air Conditioners are made up of two fundamental units: the evaporator coil and the condensing unit. These two units can be configured as a single (or package) unit, as a "split" unit, or as a "mini-split" unit.
Single or package units combine these two components into a single physical unit, usually placed outside. Cold air is transported into your house through ductwork. Single units are more commonly used in commercial or industrial buildings than in homes.
Split units typically place the louder condensing components outdoors (this is often called the "hot" side), and the quieter evaporator coil indoors (this is often called the "cold side"). If you have a warm-air furnace, the coil will generally be integrated into your furnace. Otherwise, your air conditioner will use an air handler to distribute the newly cooled air around your house.
The mini-split is slightly different, in that it is used in residences or commercial locations which do not have ductwork to carry the cold air. As you might guess by the "mini" portion of the name, mini-splits tend to be small units, typically less than 60,000 BTUH. The "split" portion of the name indicates that the condenser unit is typically located outdoors, while the evaporator is typically located indoors.