Why are the wings of some planes changing width?
Well, yes, bigger wings to provide better lift, but the also produce more induced drag in the process.

The wings on an airliner are optimized for cruise in high subsonic and transonic flight where a slender, swept wing works well.  While this is great for cruise flight, the trade-off is this style of wing requires a very high approach speed for landings which in turn require very long runways to accelerate the airplane on to reach rotation speed for takeoff or to decelerate the aircraft on once it has landed.

The Boeing Company successfully addressed these problems in the early 1960 with the development of the 727 airplane as a regional airliner.  It made use of a type of flaps called Fowler flaps (see Fig 1) in concert with leading edge extensions.  Fowler flaps. These style of flaps consist of a series of segments attached to tracks or support linkages running chordwise, allowing the flaps segments to extend and retract by rolling along said tracks.  



Fig 1. Typical Fowler flap installation

When deployed these give the effect of changing the airfoil shape from a slender, slightly cambered airfoil into a wide airfoil with a large camber.  Fowler flaps have an additional advantage to them in that partial deployment creates a large increase in lift with limited additional drag, very useful for takeoff, while when fully deployed they create a lot of drag in addition to higher lift.