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what are these green and white and yellow bands in the Airspeed Indicator use for ?

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The FAA has a nice introduction document on flight instruments, which explains all the standard markings on a typical airspeed indicator (ASI):

Airspeed Indicator

As shown in [the figure above], ASIs on single-engine small aircraft include the following standard color-coded markings:

  • White arc—commonly referred to as the flap operating range since its lower limit represents the full flap stall speed and its upper limit provides the maximum flap speed. Approaches and landings are usually flown at speeds within the white arc.
  • Lower limit of white arc (VS0)—the stalling speed or the minimum steady flight speed in the landing configuration. In small aircraft, this is the power-off stall speed at the maximum landing weight in the landing configuration (gear and flaps down).
  • Upper limit of the white arc (VFE)—the maximum speed with the flaps extended.
  • Green arc—the normal operating range of the aircraft. Most flying occurs within this range.
  • Lower limit of green arc (VS1)—the stalling speed or the minimum steady flight speed obtained in a specified configuration. For most aircraft, this is the power-off stall speed at the maximum takeoff weight in the clean configuration (gear up, if retractable, and flaps up).
  • Upper limit of green arc (VN0)—the maximum structural cruising speed. Do not exceed this speed except in smooth air.
  • Yellow arc—caution range. Fly within this range only in smooth air and then only with caution.
  • Red line (VNE)—never exceed speed. Operating above this speed is prohibited since it may result in damage or structural failure.

(FAA Handbook - Chapter 8 - Flight Instruments, emphasis mine)

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Wikipedia has a very fine article of this subject, and by chance(?) it has the picture you posted in your question. To save the trouble of going there to check this stuff out, I've composed a simplified explanation of the markings:

(as I was writing this, Bianfable posted a much better answer, but I just could not let my effort go to waste, so I posted this anyway :)

From 0 to 250 the coloured arcs on the dial mean:

60 - beginning of the white arc:

  • flaps extended stall speed, this is the minimum speed you can fly with this plane with flaps extended (= out = down).
  • the white arc marks the speed range you can use the flaps within

65 - beginning of the green arc:

  • stall speed with flaps retracted, this is the minimum speed you can fly this plane when flaps are retracted (= up).

  • the green arc marks the speed range you can normally fly the plane in

100 - end of white arc:

  • maximum flaps extended speed, this is the fastest you can go with flaps down. If you go faster, you risk damaging the flaps or the system that moves them.

165 - end of green arc, beginning of yellow arc:

  • maximum cruising speed, this is the fastest you can safely fly this plane (with flaps retracted of course).

  • the yellow arc marks the speed range within which you can operate the plane with caution, in smooth non turbulent air and without making sudden movements of the controls. Not recommended unless you really know what you are doing.

208 - red line,end of yellow arc:

  • Never exeed speed, do not go faster or you will break the plane and kill yourself!
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    $\begingroup$ "do not go faster or you will break the plane and kill yourself!" Isn't it more of a "warranty void above this speed" thing? Just because the aircraft is unrated in that region and it being a bad idea to go there, doesn't mean you'll get killed. Risk of death doesn't equal death. $\endgroup$
    – Mast
    Feb 6, 2020 at 14:07
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    $\begingroup$ Strictly speaking you are correct @Mast , the question however is obviously of the absolute beginner level, so I took the liberty of exaggerating on the safer side of things. A beginner pilot, when flying past the redline is in imminent risk of death. Sudden and large control deflections can easily break up or seriously damage an airframe, and very few beginner pilots have silky smooth touch... $\endgroup$
    – Jpe61
    Feb 6, 2020 at 14:49
  • $\begingroup$ @Jpe61 I've just found this question as an instructor under training for FI(S)! Also, beginner or otherwise, anyone who's going to be flying beyond VA ought to know what to do when facing a situation where they can't avoid busting VNE without busting G-limits. Instilling the idea that both "will" break the aircraft apart isn't exactly helpful. $\endgroup$
    – Toby Wilson
    Feb 12, 2020 at 14:26
  • $\begingroup$ Congrats on your future FI(S)! As I stated above, the question is very, very, very basic. Such questions certainly deserve an answer, I've decided my answer will also be very, very, very basic (some here downvote or vote to close basic questions rather than bothering to answer, not me (usually)). By the time an aspiring pilot gets to control a plane, the V's surely have been properly introduced. $\endgroup$
    – Jpe61
    Feb 12, 2020 at 14:48

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