An invoice is exactly the same in any country. It is a proof of purchase. That's why it's required when making a warranty claim, it proves the person is the original purchaser and it was purchased as a new product and it shows the date it was purchased and that then determines whether of not a warranty is valid.
Now in some cases in some countries, an invoice (proof of purchase) can be enough to claim a warranty. However, on products that actually come with a specific warranty document, then that document must be used along with the invoice (proof of purchase) to file a claim. Having one without the other, as it is in Turkey, will mean a warranty claim can be rejected.
Of course different countries have different protective consumer rights in place as well. So this can give the consumer an added layer of protection when they have a problem. They may not even have to file a warranty claim, the supplier may in fact just replace or refund on the spot, but that comes down to what the consumer rights and the suppliers policies actually are.