GTIN stands for Global Trade Item Number and is the number that appears in your products' barcode
GTIN is an international standard used to identify physical products. For example, if you buy a LEGO package, you can identify it with the barcode/GTIN. As a webshop owner, there isn't a big advantage for you, but it's a huge advantage for Google that you provide the product's GTIN number, as they are then able to make a price comparison across many shops.
In relation to your Google Shopping feed, it is also an advantage to enter the GTIN of your products. In Shoporama, you do this under the "Inventory management" tab. Note that products with variants (e.g. small, medium and large) will have different GTINs. This means you need to enter the GTIN of all variants. A lot of work - but reportedly it pays off in Google Shopping.
If you have special products or products you manufacture yourself, they may not have a GTIN. You can enter the MPN in Shoporama instead.
We've been working with online marketing ourselves for decades. As the only shop system in the country, we have spoken multiple times at conferences such as Marketingcamp, SEOday, Shopcamp, Digital Marketing, E-commerce Manager, Ecommerce Day, Web Analytics Wednesday and many more.