The Angle of Attack is the angle at which relative wind meets an Aerofoil. It is the angle formed by the Chord of the aerofoil and the direction of the relative wind or the vector representing the relative motion between the aircraft and the atmosphere.
The angle of attack can be simply described as the difference between where a wing is pointing and where it is going.
An increase in angle of attack results in an increase in both lift and induced drag, up to a point. Too high an angle of attack (usually around 17 degrees) and the airflow across the upper surface of the aerofoil becomes detached, resulting in a loss of lift, otherwise known as a Stall.
Note: the above diagram is sometimes referred to as the "Lift Curve"
Vmc Training and Angle of Attack, FAA, General Aviation Joint Steering Committee (GAJSC) Leaflet, November 2015 (Information on engine failure procedures for multi-engine aircraft and how angle of attack (AOA) indicator systems can help prevent stall/spin accidents)