The Ram Air Turbine, commonly referred to as RAT is a small turbine(propeller) connected to  an electric generator installed in a plane or on the plane’s hydraulic system. Modern airplanes rely on power from the main engines and usually have a backup fuel-burning engine called the auxiliary power unit. In case of a failure from these two power sources while still in flight, the RAT is deployed from either the fuselage or the wing of an airplane to serve as an emergency power supply.
Since it is only released when the plane is in flight and is still moving, the RAT is able to rotate due to the pressure (ram pressure) caused by the speed of plane, and therefore it runs the backup generator. The ram pressure is created by the flow of air (airstream), which is created by the speed of the plane, to rotate the backup generator. This backup generator is different from the primary and auxiliary engines as it relies on the rotation of the RAT to generate power for the plane (Moir & Seabridge, 2011).
The RAT in A320 is connected to the plane’s hydraulic system called the Blue HS. Its rotation pressurizes the hydraulic system hence driving the backup generator. This generator produces the required emergency power. This emergency power is used to regain control of the airplane and guide it safely to landing. It is used to power only the critical systems of the plane such as the flight controls, some vital instrumentations needed for flight generally the Primary Flight Displays and also the linked hydraulics. The reason some aircraft models such as the B737 do not have RAT is because they do not rely on electrical systems to operate (Moir & Seabridge, 2011).

References

Moir, I., & Seabridge, A. (2011). Aircraft Systems: Mechanical, Electrical and Avionics Subsystems Integration. Michigan: John Wiley & Sons.