A modern aircraft are designed to fly fast with the use of least amount of thrust, but it should also be able to fly slow enough to use relatively short runways for take-off and landing. However, the use of large wings for low speed produces high drag at high speed which presents a conflicting situation for the designer. A solution is to use so-called high lift devices.
Since one of the main goals which need to be achieved during the airplane design process is its ability to use short runways, it is necessary for the wing to produce much more lift in take-off and landing phase of flight than in rest of flight. This can be achieved in two ways: by using flaps and by using slats.

Trailing edge flaps

By adherence to the basic aerodynamics equation, the true airspeed, wing surface, air density and aerodynamic lift coefficient have a direct influence on total aerodynamic lift force. One goal is to use shorter runways which means the aircraft must take off with a lower airspeed.The only way to achieve this is by increasing aerodynamic lift coefficients since air density is constant and wing surface is practically constant (not in all cases).
If a pilot extends flaps, he actually increases a chamber of a wing section which has a direct influence on aerodynamic lift coefficient.
Flaps extension increases aerodynamic lift coefficient but it also increases aerodynamic drag coefficient which leads to increase in total aerodynamic drag. That is why before take-off, pilot extends flaps much less than in landing.
During the research process, scientists have concluded that flaps extension increases maximum lift coefficient but it also decreases the critical angle of attack (the biggest angle between free undisturbed air stream and the chord line of an airfoil where the wing will not stall). This in practical terms is a good thing since it allows pilot a better visibility from the cockpit during take-off and landing.
There are several different solutions for flaps and they are presented in the table below. Some increase camber of an airfoil but decrease wing surface (plain flap), some do not affect wing surface (split flap) and some even increase wing surface (Fowler flap). It is necessary to say that usually for basic airfoil, the maximum angle of attack is about 15ยบ.