Notice this part I circled. I don’t get what the function of this part is. can anyone tell me what good this part is? http://www.mediafire.com/view/lcuj1bqb1ki1crd/Capture.PNG
That’s the coaster brake. It’s what causes the bike to stop when you backpedal. But it’s not part of the tire, it’s part of the wheel. More specifically, part of the hub.
Does your bike have a hub brake (‘coaster brake’)? If so, I’d say it’s the brake arm.
EDIT: Dammit, Doug K.! Well, it serves me right for looking for a cite. 
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It looks like the arm of a coaster brake.
But in real life, (unlike your pic) that piece has to be connected to the frame of the bike.
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You must have hit “submit” at the same time I did. Your reply showed up immediately after mine when I hit “submit”.
Of greater curiosity, where’s the sprocket gone?
When you apply a coaster brake the wheel (driven by the inertia of you and your bike) is being connected through the friction part of the brake to the inner part of the hub. This applies tremendous amounts of torque to the inner hub.
That arm is strongly connected to the inner hub and reaches out to attach to the frame. This takes the strain from the torque on the inner hub and applies it safely to the frame. Without the arm, application of the coaster brake would twist the axle in the dropouts.