Stickers are cosmetic items that you can use to decorate your car and make it "purr-fect" looking. You can apply as many stickers as you want to your vehicle.
You get your first Sticker by completing the tutorial. After that, new Stickers will be available by completing Stages and gaining Prestige statuses.
As other items in your Garage, Stickers can be sold for Gold.
Stickers do not influence your chances of getting better quality parts or their quantity. They are simply decorative.