What is the default category of a product?
A product can belong to several categories. In PrestaShop 1.6, the product assignation to one or several categories is possible through the "Associations" tab of your back office product file. In 1.7 version, this is through the "Basic settings" tab in the "Categories" section of the right column.
In the example above in PrestaShop 1.6, the "printed summer dress" product belongs to several categories : "Home", "Women", "Dresses" and "Summer dresses". But, it's the "Summer dresses" that is the default category.
Similarly, above, in PrestaShop 1.7, the "Colibri notebook" product belongs to the "Home", "Accessories" and "Stationery" categories but it's the "Stationery" category that is the main category (i.e the default category).
For example, for the Google Merchant Center module, the Google tag assignation (material, pattern tag,...) will be made from the default product categories (all products whose default category is the one displayed will have the same tag value, for an example, click here). Then, before configuring a tag for each of your categories, it's important you make sure that, for each of the products you want to display on Google Shopping, you well defined a default category and that this is relevant regarding the product nature. Do not make your choice at random, please keep in mind that all the products of a this category will have the same Google tag.