During takeoff and landing an airplane it is at its lowest flight velocity. Stalling speed of an aircraft is the minimum speed at which it can fly in a straight and level flight. At stalling speed, an aircraft is flying at an angle of attack which produces maximum coefficient of lift.

An airplane during takeoff with flaps down

So, if we want to have a decrease in stall velocity, we need to increase more coefficient of lift of the airfoil. A wing with a given airfoil shape has a fixed maximum coefficient of lift, which is dependent on the nature of flow physics over the airfoil. In order to increase the coefficient of lift, artificial high lifting devices are used. Flaps are the high lift devices that are located at the trailing edge of the wing.

Flaps increase the lift coefficient when it is deflected downwards. Flaps increase the camber as well as the chord of the airfoil, resulting in an increase in coefficient of lift.

The following sequence is in increasing order of maximum coefficient of lift produced by flaps and addition of other high lift devices. Plain flap < split flap <airfoil with a leading edge slat < airfoil with a single-slotted flap < airfoil with a double slotted flap < airfoil with a double slotted flap and a slat < airfoil with a boundary-layer suction at top of the airfoil. 

So flaps increase the maximum lift coefficient of an airfoil, which can be used to reduce the take-off and landing distance.

Flap during flight