When an airplane takes off its wings generate lift as air flows over the wings. The wing surface curved, so air moving of the top of the wing goes faster than air flowing under the bottom of the wing which is flat. There's more pressure under the wing than on top, so the wing (and the airplane) generate lift and can fly. When an airplane gets going to a speed that's close to the speed of sound it can start to shake this is the result of a shock wave behind the wing when the air moving over the top exceeds the speed of sound. For airplanes to go faster than the speed of sound, a new type of wing was invented.
Swept wings are wings which are angled back from the body of the plane, also know as the fuselage. Instead of changing the curve of the wing to reduce the shock wave (which creates drag on the body of the airplane) inventors decided to sweep the wings back to create the illusion that the wing is longer than it actually is. Since the air travels further and over a flatter wing surface the shock wave and drag is reduced. This saves energy and makes the airplane more efficient in flight.
But even though the swept wing has advantages during flight speeds greater than the speed of sound, it has disadvantages too. At speeds significantly slower than the speed of sound swept wings can actually create more drag because of the very fact that they "trick" the air flow into moving over a longer wing, so swept wings are only more efficient at supersonic speeds.
Swept wings were first designed during the second World War by the Germans and the design was later copied by other countries, including Great Britain, France, and the United States. Swept wings can be seen on most aircraft today, since most aircraft fly at speeds approaching or passing the speed of sound. Smaller aircraft which tend to still fly at slower speeds (less than a few hundered miles per hour) usually have traditional wings.