In airfoil design, camber is a dissymmetry between the upper and lower defining curves of an airfoil. Typically, this involves having a normal upper curve while modifying the lower curve so it comes closer to the chord line. A symmetric airfoil is symmetric over the chord line. The lower curve will have a point of inflection.
Cambering an airfoil is done to provide positive lift at zero angle of attack. The effect is due to Bernoulli's Principle and the Continuity Equation, which summarizes to: the air flowing over the top of the wing will have greater velocity and thus lower pressure than the air flowing under the wing, and this pressure difference produces lift. A symmetric airfoil, that is, one with no camber, will not have lift at zero angle of attack because the path above and below the airfoil is the same. However, the shorter path provided under a wing by a cambered airfoil allows lift to be generated, even if the wing is not angled upward.
Cambered airfoils are used on most modern aircraft. Exceptions are aerobatic craft, such as the Extra 300, and military fighters. These types of aircraft need to be able to perform unusual manuvers, notably, flying knife edge, where the fuselage produces lift and a cambered wing would cause the plane to yaw, or flying upside-down, where a cambered wing would just make the plane decend.
The high-lift systems on airliners and cargo airplanes, consisting of flaps and slats, is actually just a conspiracy to increase the apparent camber of the wings so the airplane can takeoff at a lower speed. However, such a heavily cambered wing will stall at a much lower angle of attack, and is less efficient, which is why the flaps and slats are retracted soon after the airplane leaves the ground.