FLAPS 0 can used for a higher approach speed when
there is wind. This "clean" configuration will give you the greatest gliding distance (least drag per distance flown). Approach speeds are higher and the glide angle is flatter. This is fine when one has adequate runway to work with. With 0 flaps, the wing has less camber and lower coefficient of lift. It makes up for this by going a bit faster.
Flaps 10 is used for short field approaches. It increases wing camber and coefficient of lift, allowing the aircraft to approach around at a slower speed while still generating adequate lift. Because there is greater drag, the glide angle will be slightly steeper. Better to use this one if the landing area is shorter.
FLAPS 20, 30 (and 40) serve to further steeper the glide angle by increasing drag. These flap settings generally do not increase lift much more and are not used for that purpose because they are excessively draggy.
FLAPS 10 can also be used for short, soft field takeoffs, but the plane climbs more efficiently at Vy, with FLAPS 0.
More reading about flaps here.
Another way of looking at it is: increasing coefficient of lift by increasing camber allows one to fly at the same Angle of Attack at a lower airspeed.
Angle of Attack and Camber form the Lift Coefficient. Too great and angle of attack causes a stall, so it is smarter to increase camber to fly more safely at a lower airspeed.
The variables of lift related to aircraft configuration and velocity are explained in the Lift Equation:
Lift = Density × Area × Lift Coefficient × Velocity$^2$.
Note that velocity is squared.