Stickers are cosmetic items that you can use to decorate your car and make it "purr-fect" looking. You can put as many stickers on your car as you like.
You get your first sticker by completing the tutorial. After that, new stickers will be available by completing stages and gaining Prestige levels.
Like other items in your garage, stickers can be sold for gold.
Stickers do not affect your chances of getting better quality parts or the quantity of parts you get. They are simply decorative.