QDM
Flaps come in a variety of shapes and sizes but consider the Fowler flaps on a Cessna. They increase wing area and camber, thus increasing coefficient of lift. From the lift formula it can be seen that with an increase in S (wing area) and Cl, the same amount of lift can be generated at a lower V (very useful for approach to land). It also means that more lift will be generated for any given angle of attack than for a clean wing, hence a better view of the runway.
Another side effect of flap deployment is that the wing will stall at a lower AofA than clean due to the increase in induced drag as speed reduces. This is partially countered on transport aircraft with the use of leading edge devices to re-energise the boundary layer over the upper surface of the wing but these are not found on most typical training aircraft.
If you still don't believe me, next time you go flying try some stalls (at a safe height, of course!) with and without flap and note the result.