What GTIN means
GTIN stands for Global Trade Item Number, the standard identifier that GS1 (the international organisation that manages barcode systems) assigns to a product to distinguish it from every other product on the market. It is the number encoded under the barcode, commonly known as a UPC or an EAN depending on the region and the format.
Each variant of a product, such as the same model in a different colour, size or fill volume, needs its own GTIN. A GTIN does not describe the product in text: it does not say whether it is a blue T-shirt or a 50 ml face cream. What it does is give that specific product a number that any system, from a checkout till to the Google Shopping catalogue, can read and recognise without ambiguity.
It is worth distinguishing the GTIN from the SKU. The SKU is an internal code each store invents for its own inventory, and it can repeat or change from one store to another. The GTIN is assigned by GS1, or by the manufacturer under licence from GS1, and it stays the same in every store worldwide that sells that product. One is private, the other is universal.
The same GTIN travels with the product throughout its entire commercial life: it appears on the manufacturer's invoice, on the warehouse delivery note, and on the checkout receipt, always as the same number. That persistence is what lets systems run by different companies, which never coordinated with each other, refer to the same product without ambiguity.